Solve Using the Quadratic Formula 5x^2+9x-72=0

$5 x^{2} + 9 x - 72 = 0$

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 $a = 5$ , $b = 9$ , and $c = - 72$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (5 \cdot - 72)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 5 \cdot - 72}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 72$ .

Multiply $- 4$ by $5$ .

$x = \frac{- 9 \pm \sqrt{81 - 20 \cdot - 72}}{2 \cdot 5}$

Multiply $- 20$ by $- 72$ .

$x = \frac{- 9 \pm \sqrt{81 + 1440}}{2 \cdot 5}$

Add $81$ and $1440$ .

$x = \frac{- 9 \pm \sqrt{1521}}{2 \cdot 5}$

Rewrite $1521$ as $39^{2}$ .

$x = \frac{- 9 \pm \sqrt{39^{2}}}{2 \cdot 5}$

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

$x = \frac{- 9 \pm 39}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 9 \pm 39}{10}$

Step 4

The final answer is the combination of both solutions.

$x = 3, - \frac{24}{5}$