Solve Using the Quadratic Formula 2x^2-9x-3=0

$2 x^{2} - 9 x - 3 = 0$

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 $a = 2$ , $b = - 9$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (2 \cdot - 3)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 2 \cdot - 3}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{9 \pm \sqrt{81 - 8 \cdot - 3}}{2 \cdot 2}$

Multiply $- 8$ by $- 3$ .

$x = \frac{9 \pm \sqrt{81 + 24}}{2 \cdot 2}$

Add $81$ and $24$ .

$x = \frac{9 \pm \sqrt{105}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{9 \pm \sqrt{105}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9 \pm \sqrt{105}}{4}$

Decimal Form:

$x = 4.81173769 \dots, - 0.31173769 \dots$