Solve Using the Quadratic Formula 15x^2+58x+48=0

$15 x^{2} + 58 x + 48 = 0$

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 $a = 15$ , $b = 58$ , and $c = 48$ into the quadratic formula and solve for $x$ .

$\frac{- 58 \pm \sqrt{58^{2} - 4 \cdot (15 \cdot 48)}}{2 \cdot 15}$

Step 3

Simplify.

Simplify the numerator.

Raise $58$ to the power of $2$ .

$x = \frac{- 58 \pm \sqrt{3364 - 4 \cdot 15 \cdot 48}}{2 \cdot 15}$

Multiply $- 4 \cdot 15 \cdot 48$ .

Multiply $- 4$ by $15$ .

$x = \frac{- 58 \pm \sqrt{3364 - 60 \cdot 48}}{2 \cdot 15}$

Multiply $- 60$ by $48$ .

$x = \frac{- 58 \pm \sqrt{3364 - 2880}}{2 \cdot 15}$

Subtract $2880$ from $3364$ .

$x = \frac{- 58 \pm \sqrt{484}}{2 \cdot 15}$

Rewrite $484$ as $22^{2}$ .

$x = \frac{- 58 \pm \sqrt{22^{2}}}{2 \cdot 15}$

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

$x = \frac{- 58 \pm 22}{2 \cdot 15}$

Multiply $2$ by $15$ .

$x = \frac{- 58 \pm 22}{30}$

Simplify $\frac{- 58 \pm 22}{30}$ .

$x = \frac{- 29 \pm 11}{15}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{6}{5}, - \frac{8}{3}$