Solve Using the Quadratic Formula 6x^2+9x=-1

$6 x^{2} + 9 x = - 1$

Step 1

Add $1$ to both sides of the equation.

$6 x^{2} + 9 x + 1 = 0$

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 $a = 6$ , $b = 9$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (6 \cdot 1)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 6 \cdot 1}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot 1$ .

Multiply $- 4$ by $6$ .

$x = \frac{- 9 \pm \sqrt{81 - 24 \cdot 1}}{2 \cdot 6}$

Multiply $- 24$ by $1$ .

$x = \frac{- 9 \pm \sqrt{81 - 24}}{2 \cdot 6}$

Subtract $24$ from $81$ .

$x = \frac{- 9 \pm \sqrt{57}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 9 \pm \sqrt{57}}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 9 \pm \sqrt{57}}{12}$

Decimal Form:

$x = - 0.12084713 \dots, - 1.37915286 \dots$