Solve Using the Quadratic Formula 3x^2-3x-7=0

$3 x^{2} - 3 x - 7 = 0$

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 $a = 3$ , $b = - 3$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (3 \cdot - 7)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 3 \cdot - 7}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 7$ .

Multiply $- 4$ by $3$ .

$x = \frac{3 \pm \sqrt{9 - 12 \cdot - 7}}{2 \cdot 3}$

Multiply $- 12$ by $- 7$ .

$x = \frac{3 \pm \sqrt{9 + 84}}{2 \cdot 3}$

Add $9$ and $84$ .

$x = \frac{3 \pm \sqrt{93}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{3 \pm \sqrt{93}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 \pm \sqrt{93}}{6}$

Decimal Form:

$x = 2.10727512 \dots, - 1.10727512 \dots$