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

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

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

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $- 3$ .

$x = \frac{- 9 \pm \sqrt{81 + 12 \cdot - 2}}{2 \cdot - 3}$

Multiply $12$ by $- 2$ .

$x = \frac{- 9 \pm \sqrt{81 - 24}}{2 \cdot - 3}$

Subtract $24$ from $81$ .

$x = \frac{- 9 \pm \sqrt{57}}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{- 9 \pm \sqrt{57}}{- 6}$

Simplify $\frac{- 9 \pm \sqrt{57}}{- 6}$ .

$x = \frac{9 \pm \sqrt{57}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9 \pm \sqrt{57}}{6}$

Decimal Form:

$x = 2.75830573 \dots, 0.24169426 \dots$