Solve Using the Quadratic Formula f(x)=-3x^2+9x

$f (x) = - 3 x^{2} + 9 x$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 3$ , $b = 9$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (- 3 \cdot 0)}}{2 \cdot - 3}$

Simplify.

Simplify the numerator.

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

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot - 3 \cdot 0}}{2 \cdot - 3}$

Multiply $- 4$ by $- 3$ .

$x = \frac{- 9 \pm \sqrt{81 + 12 \cdot 0}}{2 \cdot - 3}$

Multiply $12$ by $0$ .

$x = \frac{- 9 \pm \sqrt{81 + 0}}{2 \cdot - 3}$

Add $81$ and $0$ .

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

Rewrite $81$ as $9^{2}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

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

Multiply $2$ by $- 3$ .

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

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

$x = \frac{3 \pm 3}{2}$

The final answer is the combination of both solutions.

$x = 3, 0$