Solve for x 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 $- 2$ .

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

Add $49$ and $48$ .

$x = \frac{- 7 \pm \sqrt{97}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 7 \pm \sqrt{97}}{12}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{7 - \sqrt{97}}{12}, - \frac{7 + \sqrt{97}}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7 - \sqrt{97}}{12}, - \frac{7 + \sqrt{97}}{12}$

Decimal Form:

$x = 0.23740481 \dots, - 1.40407148 \dots$