Solve Using the Quadratic Formula 6x^2-2x=7

$6 x^{2} - 2 x = 7$

Step 1

Subtract $7$ from both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 6 \cdot - 7$ .

Multiply $- 4$ by $6$ .

$x = \frac{2 \pm \sqrt{4 - 24 \cdot - 7}}{2 \cdot 6}$

Multiply $- 24$ by $- 7$ .

$x = \frac{2 \pm \sqrt{4 + 168}}{2 \cdot 6}$

Add $4$ and $168$ .

$x = \frac{2 \pm \sqrt{172}}{2 \cdot 6}$

Rewrite $172$ as $2^{2} \cdot 43$ .

Factor $4$ out of $172$ .

$x = \frac{2 \pm \sqrt{4 (43)}}{2 \cdot 6}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} \cdot 43}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{2 \pm 2 \sqrt{43}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{2 \pm 2 \sqrt{43}}{12}$

Simplify $\frac{2 \pm 2 \sqrt{43}}{12}$ .

$x = \frac{1 \pm \sqrt{43}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{43}}{6}$

Decimal Form:

$x = 1.25957308 \dots, - 0.92623975 \dots$