Solve Using the Quadratic Formula 2x^2=5x+11

$2 x^{2} = 5 x + 11$

Step 1

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

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

$2 x^{2} - 5 x = 11$

Subtract $11$ from both sides of the equation.

$2 x^{2} - 5 x - 11 = 0$

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 $a = 2$ , $b = - 5$ , and $c = - 11$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (2 \cdot - 11)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 2 \cdot - 11}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 11$ .

Multiply $- 4$ by $2$ .

$x = \frac{5 \pm \sqrt{25 - 8 \cdot - 11}}{2 \cdot 2}$

Multiply $- 8$ by $- 11$ .

$x = \frac{5 \pm \sqrt{25 + 88}}{2 \cdot 2}$

Add $25$ and $88$ .

$x = \frac{5 \pm \sqrt{113}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{5 \pm \sqrt{113}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 \pm \sqrt{113}}{4}$

Decimal Form:

$x = 3.90753645 \dots, - 1.40753645 \dots$