Find the Roots (Zeros) 2x^2=5x+2

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

Step 1

Subtract $5 x$ from both sides of the equation.

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

Step 2

Subtract $2$ from both sides of the equation.

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

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

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

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

Step 5

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $2$ .

$x = \frac{5 \pm \sqrt{25 - 8 \cdot - 2}}{2 \cdot 2}$

Multiply $- 8$ by $- 2$ .

$x = \frac{5 \pm \sqrt{25 + 16}}{2 \cdot 2}$

Add $25$ and $16$ .

$x = \frac{5 \pm \sqrt{41}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{5 \pm \sqrt{41}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 \pm \sqrt{41}}{4}$

Decimal Form:

$x = 2.85078105 \dots, - 0.35078105 \dots$

Step 7