Solve for x -5x^2-6=-4x

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

Step 1

Add $4 x$ to both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

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

Multiply $- 4 \cdot - 5 \cdot - 6$ .

Multiply $- 4$ by $- 5$ .

$x = \frac{- 4 \pm \sqrt{16 + 20 \cdot - 6}}{2 \cdot - 5}$

Multiply $20$ by $- 6$ .

$x = \frac{- 4 \pm \sqrt{16 - 120}}{2 \cdot - 5}$

Subtract $120$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 104}}{2 \cdot - 5}$

Rewrite $- 104$ as $- 1 (104)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 104}}{2 \cdot - 5}$

Rewrite $\sqrt{- 1 (104)}$ as $\sqrt{- 1} \cdot \sqrt{104}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{104}}{2 \cdot - 5}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 4 \pm i \cdot \sqrt{104}}{2 \cdot - 5}$

Rewrite $104$ as $2^{2} \cdot 26$ .

Factor $4$ out of $104$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (26)}}{2 \cdot - 5}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 26}}{2 \cdot - 5}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{26})}{2 \cdot - 5}$

Move $2$ to the left of $i$ .

$x = \frac{- 4 \pm 2 i \sqrt{26}}{2 \cdot - 5}$

Multiply $2$ by $- 5$ .

$x = \frac{- 4 \pm 2 i \sqrt{26}}{- 10}$

Simplify $\frac{- 4 \pm 2 i \sqrt{26}}{- 10}$ .

$x = \frac{2 \pm i \sqrt{26}}{5}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{2 + i \sqrt{26}}{5}, \frac{2 - i \sqrt{26}}{5}$