Solve Using the Quadratic Formula 6x^2-12x+1=0

$6 x^{2} - 12 x + 1 = 0$

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 $a = 6$ , $b = - 12$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{12 \pm \sqrt{{(- 12)}^{2} - 4 \cdot (6 \cdot 1)}}{2 \cdot 6}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 12$ to the power of $2$ .

$x = \frac{12 \pm \sqrt{144 - 4 \cdot 6 \cdot 1}}{2 \cdot 6}$

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

Multiply $- 4$ by $6$ .

$x = \frac{12 \pm \sqrt{144 - 24 \cdot 1}}{2 \cdot 6}$

Multiply $- 24$ by $1$ .

$x = \frac{12 \pm \sqrt{144 - 24}}{2 \cdot 6}$

Subtract $24$ from $144$ .

$x = \frac{12 \pm \sqrt{120}}{2 \cdot 6}$

Rewrite $120$ as $2^{2} \cdot 30$ .

Factor $4$ out of $120$ .

$x = \frac{12 \pm \sqrt{4 (30)}}{2 \cdot 6}$

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

$x = \frac{12 \pm \sqrt{2^{2} \cdot 30}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{12 \pm 2 \sqrt{30}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{12 \pm 2 \sqrt{30}}{12}$

Simplify $\frac{12 \pm 2 \sqrt{30}}{12}$ .

$x = \frac{6 \pm \sqrt{30}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6 \pm \sqrt{30}}{6}$

Decimal Form:

$x = 1.91287092 \dots, 0.08712907 \dots$