# Know About Quadratic Equation: 4x ^ 2 - 5x - 12=0

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Mathematics is full of quadratic and algebraic equation, and 4x ^ 2 - 5x - 12=0 is also one of them. In the below article, we are going explain how you can solve this quadratic equation. This equation looks complicated as we have to find out the answer for x but when you start solving it, you will find it is the easiest one out there.

Let’s read the below article where you can find step-by-step instructions to solve it. So, look below:

### Know what are quadratic equations?

Let us tell you that quadratic equations are second-degree polynomial equations. It means it contains the variables raised by the two powers. Simply put, the quadratic equation is mainly written like this 4x ^ 2 - 5x - 12=0 format where you can find a, b, and c as coefficients. Here, you need to find the solution to the x variable by solving this equation.

### Characteristics of the 4x ^ 2 - 5x - 12=0 quadratic equation

If you see on this quadratic equation, you may find it difficult. Let’s check what it is actually. This equation showcases some characteristics fundamental to the solution and even study. It is made of a parabolic shape and a vertex which represent the minimum and maximum points. If you understand these characteristics, it helps you enhance your practical solution power and insights.

### Methods to solve quadratic equation: 4x ^ 2 - 5x - 12=0

Let’s check out different methods to solve 4x ^ 2 - 5x - 12=0 quadratic equation in the below segment:

#### Factoring method:

In this factoring method, there are two factors to solve this quadratic equation. To solve it, you need to discover binomials. With the help of these binomials, you can provide the quadratic equation by multiplying them together. Now, you will receive a certain equation, i.e., (2X+3)(2X-4)=0. Next, you must make each equation equal to 0. After this step, you will receive more 2 equations, such as 2x + 3 = 0 & 2x – 4 = 0. After solving them, you will get the answer of x and the answer will be x = -3/2 and x = 2.

It is another method to solve the 4x ^ 2 - 5x - 12=0. It is known as the most reliable method. So, let's check it.

We use the quadratic formula that is x = (-b ± √(b^2 – 4ac)) / 2a to solve 4x ^ 2 - 5x - 12=0. Place the values a = 4, B, and c=12 in this formula then calculate it. After calculating, you will find x = -3/2 and x = 2 is the solution for this quadratic equation.

#### Conclusion:

We have discussed two primary methods to solve the 4x ^ 2 - 5x - 12=0 quadratic equation in this article. You can check both methods in this article and effectively solve this quadratic equation easily. One more thing discuss, these methods can be employed by any students due to its simplicity.