Solve Using the Quadratic Formula 5-2x^2=6x

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

Step 1

Subtract $6 x$ from both sides of the equation.

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

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 $a = - 2$ , $b = - 6$ , and $c = 5$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot - 2 \cdot 5}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot 5$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{6 \pm \sqrt{36 + 8 \cdot 5}}{2 \cdot - 2}$

Multiply $8$ by $5$ .

$x = \frac{6 \pm \sqrt{36 + 40}}{2 \cdot - 2}$

Add $36$ and $40$ .

$x = \frac{6 \pm \sqrt{76}}{2 \cdot - 2}$

Rewrite $76$ as $2^{2} \cdot 19$ .

Factor $4$ out of $76$ .

$x = \frac{6 \pm \sqrt{4 (19)}}{2 \cdot - 2}$

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

$x = \frac{6 \pm \sqrt{2^{2} \cdot 19}}{2 \cdot - 2}$

Pull terms out from under the radical.

$x = \frac{6 \pm 2 \sqrt{19}}{2 \cdot - 2}$

Multiply $2$ by $- 2$ .

$x = \frac{6 \pm 2 \sqrt{19}}{- 4}$

Simplify $\frac{6 \pm 2 \sqrt{19}}{- 4}$ .

$x = \frac{3 \pm \sqrt{19}}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{3 \pm \sqrt{19}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3 \pm \sqrt{19}}{2}$

Decimal Form:

$x = - 3.67944947 \dots, 0.67944947 \dots$