Solve Using the Quadratic Formula 8n^2+7n-15=-7

$8 n^{2} + 7 n - 15 = - 7$

Step 1

Move all terms to the left side of the equation and simplify.

Add $7$ to both sides of the equation.

$8 n^{2} + 7 n - 15 + 7 = 0$

Add $- 15$ and $7$ .

$8 n^{2} + 7 n - 8 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 8$ , $b = 7$ , and $c = - 8$ into the quadratic formula and solve for $n$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (8 \cdot - 8)}}{2 \cdot 8}$

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$n = \frac{- 7 \pm \sqrt{49 - 4 \cdot 8 \cdot - 8}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 8$ .

Multiply $- 4$ by $8$ .

$n = \frac{- 7 \pm \sqrt{49 - 32 \cdot - 8}}{2 \cdot 8}$

Multiply $- 32$ by $- 8$ .

$n = \frac{- 7 \pm \sqrt{49 + 256}}{2 \cdot 8}$

Add $49$ and $256$ .

$n = \frac{- 7 \pm \sqrt{305}}{2 \cdot 8}$

Multiply $2$ by $8$ .

$n = \frac{- 7 \pm \sqrt{305}}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{- 7 \pm \sqrt{305}}{16}$

Decimal Form:

$n = 0.65401557 \dots, - 1.52901557 \dots$