Solve Using the Quadratic Formula 4x^2-69x-54=0

$4 x^{2} - 69 x - 54 = 0$

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 $a = 4$ , $b = - 69$ , and $c = - 54$ into the quadratic formula and solve for $x$ .

$\frac{69 \pm \sqrt{{(- 69)}^{2} - 4 \cdot (4 \cdot - 54)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 69$ to the power of $2$ .

$x = \frac{69 \pm \sqrt{4761 - 4 \cdot 4 \cdot - 54}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 54$ .

Multiply $- 4$ by $4$ .

$x = \frac{69 \pm \sqrt{4761 - 16 \cdot - 54}}{2 \cdot 4}$

Multiply $- 16$ by $- 54$ .

$x = \frac{69 \pm \sqrt{4761 + 864}}{2 \cdot 4}$

Add $4761$ and $864$ .

$x = \frac{69 \pm \sqrt{5625}}{2 \cdot 4}$

Rewrite $5625$ as $75^{2}$ .

$x = \frac{69 \pm \sqrt{75^{2}}}{2 \cdot 4}$

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

$x = \frac{69 \pm 75}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{69 \pm 75}{8}$

Step 4

The final answer is the combination of both solutions.

$x = 18, - \frac{3}{4}$