Solve Using the Quadratic Formula 6x^2+7x+2=0

$6 x^{2} + 7 x + 2 = 0$

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 $a = 6$ , $b = 7$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (6 \cdot 2)}}{2 \cdot 6}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 6 \cdot 2}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot 2$ .

Multiply $- 4$ by $6$ .

$x = \frac{- 7 \pm \sqrt{49 - 24 \cdot 2}}{2 \cdot 6}$

Multiply $- 24$ by $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 48}}{2 \cdot 6}$

Subtract $48$ from $49$ .

$x = \frac{- 7 \pm \sqrt{1}}{2 \cdot 6}$

Any root of $1$ is $1$ .

$x = \frac{- 7 \pm 1}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 7 \pm 1}{12}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{1}{2}, - \frac{2}{3}$