Question

Solve the equation.

$6x^2-5x-4=0$

Short answer

The solutions of the given equation are $x=\frac{4}{3},-\frac{1}{2}$.

Step-by-step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $"="$.

Step 2. Write the standard form of a quadratic equation.

The standard form of a quadratic equation is given by

$a{x}^2+bx+c=0$, where$a\ne 0$

Step 3. Solve the equation 6x2−5x−4=0.

$$\begin{gathered} 6x^2-5x-4=0 \\ 6x^2-8x+3x-4=0 \\ 2x\left(3x-4\right)+1\left(3x-4\right)=0 \\ \left(3x-4\right)\left(2x+1\right)=0 \end{gathered}$$

$3x-4=0$or $2x+1=0$

$3x=4$or$2x=-1$

$x=\frac{4}{3}$or$x=-\frac{1}{2}$

$x=\frac{4}{3},-\frac{1}{2}$

Therefore the solutions of the given equation are $x=\frac{4}{3},-\frac{1}{2}$.