Solve Using the Quadratic Formula 2x^2+5x-9=0

$2 x^{2} + 5 x - 9 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 2$ , $b = 5$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (2 \cdot - 9)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 2 \cdot - 9}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 9$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 8 \cdot - 9}}{2 \cdot 2}$

Multiply $- 8$ by $- 9$ .

$x = \frac{- 5 \pm \sqrt{25 + 72}}{2 \cdot 2}$

Add $25$ and $72$ .

$x = \frac{- 5 \pm \sqrt{97}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 5 \pm \sqrt{97}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 5 \pm \sqrt{97}}{4}$

Decimal Form:

$x = 1.21221445 \dots, - 3.71221445 \dots$