Nowadays Quadratic Equation has become an important part in the syllabus of mathematics whether its School or Universities for every institution. Well many people have this thinking that Quadratic does not have any uses except in the field of mathematics but actually it is a misconception because everything learned and taught have its own important uses in other fields of study that are more direct or aligned in the research and development fields. Today in this blog we are going to have a look at what quadratic equation means and also going to solve this amazing Quadratic problem 4x ^ 2 – 5x – 12 = 0.

## 4x ^ 2 – 5x – 12 = 0 **Overview of Quadratic Equation**

The Quadratic Equation is one of the most important elements in Algebra. This algebraic category is said to be one of the most fundamental concepts and without this knowledge one may miss out a important part of their learning about an important and huge part of Mathematics. Now let’s have a look at the equation 4x ^ 2 – 5x – 12 = 0, and find out a comprehensive solution of the same.

**4x ^ 2 – 5x – 12 = 0** **Concept of Quadratic Equation**

A Quadratic Equation is also defined as a polynomial equation that is of second degree. This means the whole equation should atleast have one term that is squared.

- The general form in which quadratic equation is presented is
**ax^2 + bx + c = 0** - Here,
**a,b**and**c**are constant and**x**is represented as a variable. - We have an equation in the given form that is required to be solved.

**Q. Equation:-** 4x ^ 2 – 5x – 12 = 0

The given equation 4x ^ 2 – 5x – 12 = 0 can be solved with the help of quadratic equation formulas.

- To solve this equation we have two ways to do so.

- Direct Method
- Sridhar Acharya Method

- Since this is one of the basic equation equations, here we will go with the direct approach.

**4x ^ 2 – 5x – 12 = 0** **Solution **of the Equation

**Direct Approach**

If we are going through a direct approach then we will get two values of x. Here we have a step by step guide to solve the equation 4x ^ 2 – 5x – 12 = 0

- Step one is to note down the equation from the book or question paper into your notebook.
- Step two is to write down the equation in the form of:

4x ^ 2 – 5x – 12 = 0

- Step three is to break the middle part of the equation and it goes of like:

4x ^ 2 – 5x – 12 = 0

- Then write down the equation in the given form after taking common numbers and variables from both parts:

2x(2x-1)-3(x-4)=0

- But then as we can see the values after equating are not desirable, that’s why the equation is not valid.

**Sridhar Acharya Method**

Well we do have another way to solve this equation and that is the **Sridharacharya Method.**

- To use method we use a formula that is:

*** x=** **(-b ± √(b^2 – 4ac)) /2a**

- Here we can substitute x, a, b and c with the necessary values from the given equation and use them here in the equation.
- As moving forward you will find the necessary values

**x=****(-b ± √(b^2 – 4ac)) /2a****Put****a= 4, b= 5 and c= 12****x=****(-5 ± √(5^2 – 4x4x12)/2×4****After solving the equation, we get x= √217 +5/8 or x= –****√217 + 5/8****Calculating root value we get,****Axis of Symmetry (dashed) {x}= {0.62}****Vertex at {x,y} = {0.62,-13.56}****x- Intercepts (Roots):****Root 1 at {x,y} = {-1.22,0.00}****Root 2 at {x,y} = {2.47,0.00}**

- Hence the quadratic equation 4x^2 – 5x – 12 = 0 , has the value of x, which is x =
**5+√2178 , x =5−√2178**or**x =2.4663, x= -1.21636**

**4x ^ 2 – 5x – 12 = 0** **Diagram showing Equation**

**Root 1 at {X,Y} = {-1.22,0.00}****Root 2 at {X,Y} = {2.47,0.00}**

**Uses of Quadratic Equation**

Quadratic Equation in reality has much more use than what it may look like. The equation formula are used in other several field and here are some of the places where quadratic equation are mainly used:

**Physics**is a field where quadratic equations are used for complex and difficult calculations. The equation is used for calculating projectile motion and other topics of physics.**Engineering**is also a field where quadratic equations are used for solving equations. The equation can be for signal processing, structural analysis or can also be used for electrical circuits.**The study of Finances**is a field which uses quadratic equations in the modeling of complex financial system areas.

## Conclusion

In this article we have talked about the quadratic equation 4x ^ 2 – 5x – 12 = 0, here we have understood the concept of this equation along with the uses and solution of it. If you are someone looking for the solution of this equation or finding it critical to understand then we hope this article may help you. We have tried to gather all important information of it and hope that you find it useful.

Also, Read More About:- **ToffеeShare : How to Sharе an Infinitе Numbеr of Filеs Using**