Solve Using the Quadratic Formula f(x)=4x^2-9

$f (x) = 4 x^{2} - 9$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 4$ , $b = 0$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

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

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

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

Multiply $- 4$ by $4$ .

$x = \frac{0 \pm \sqrt{0 - 16 \cdot - 9}}{2 \cdot 4}$

Multiply $- 16$ by $- 9$ .

$x = \frac{0 \pm \sqrt{0 + 144}}{2 \cdot 4}$

Add $0$ and $144$ .

$x = \frac{0 \pm \sqrt{144}}{2 \cdot 4}$

Rewrite $144$ as $12^{2}$ .

$x = \frac{0 \pm \sqrt{12^{2}}}{2 \cdot 4}$

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

$x = \frac{0 \pm 12}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{0 \pm 12}{8}$

Simplify $\frac{0 \pm 12}{8}$ .

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

The final answer is the combination of both solutions.

$x = \frac{3}{2}, - \frac{3}{2}$