Solve Using the Quadratic Formula 2y^2+2=9y

$2 y^{2} + 2 = 9 y$

Step 1

Subtract $9 y$ from both sides of the equation.

$2 y^{2} + 2 - 9 y = 0$

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 $a = 2$ , $b = - 9$ , and $c = 2$ into the quadratic formula and solve for $y$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (2 \cdot 2)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$y = \frac{9 \pm \sqrt{81 - 4 \cdot 2 \cdot 2}}{2 \cdot 2}$

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

Multiply $- 4$ by $2$ .

$y = \frac{9 \pm \sqrt{81 - 8 \cdot 2}}{2 \cdot 2}$

Multiply $- 8$ by $2$ .

$y = \frac{9 \pm \sqrt{81 - 16}}{2 \cdot 2}$

Subtract $16$ from $81$ .

$y = \frac{9 \pm \sqrt{65}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$y = \frac{9 \pm \sqrt{65}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{9 \pm \sqrt{65}}{4}$

Decimal Form:

$y = 4.26556443 \dots, 0.23443556 \dots$