Solve Using the Quadratic Formula 4x^2+5x=6

$4 x^{2} + 5 x = 6$

Step 1

Subtract $6$ from both sides of the equation.

$4 x^{2} + 5 x - 6 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 4$ , $b = 5$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (4 \cdot - 6)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 4 \cdot - 6}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 6$ .

Multiply $- 4$ by $4$ .

$x = \frac{- 5 \pm \sqrt{25 - 16 \cdot - 6}}{2 \cdot 4}$

Multiply $- 16$ by $- 6$ .

$x = \frac{- 5 \pm \sqrt{25 + 96}}{2 \cdot 4}$

Add $25$ and $96$ .

$x = \frac{- 5 \pm \sqrt{121}}{2 \cdot 4}$

Rewrite $121$ as $11^{2}$ .

$x = \frac{- 5 \pm \sqrt{11^{2}}}{2 \cdot 4}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 5 \pm 11}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 5 \pm 11}{8}$

Step 5

The final answer is the combination of both solutions.

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