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

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

Step 1

Move all the expressions to the left side of the equation.

Subtract $5$ from both sides of the equation.

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

Add $6 x$ to both sides of the equation.

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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