Solve Using the Quadratic Formula 6x^2+x-15=8

$6 x^{2} + x - 15 = 8$

Step 1

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

Subtract $8$ from both sides of the equation.

$6 x^{2} + x - 15 - 8 = 0$

Subtract $8$ from $- 15$ .

$6 x^{2} + x - 23 = 0$

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 $a = 6$ , $b = 1$ , and $c = - 23$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (6 \cdot - 23)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 6 \cdot - 23}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 23$ .

Multiply $- 4$ by $6$ .

$x = \frac{- 1 \pm \sqrt{1 - 24 \cdot - 23}}{2 \cdot 6}$

Multiply $- 24$ by $- 23$ .

$x = \frac{- 1 \pm \sqrt{1 + 552}}{2 \cdot 6}$

Add $1$ and $552$ .

$x = \frac{- 1 \pm \sqrt{553}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 1 \pm \sqrt{553}}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{553}}{12}$

Decimal Form:

$x = 1.87632933 \dots, - 2.04299600 \dots$