Solve Using the Quadratic Formula 6x^2+1=20

$6 x^{2} + 1 = 20$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $20$ from both sides of the equation.

$6 x^{2} + 1 - 20 = 0$

Subtract $20$ from $1$ .

$6 x^{2} - 19 = 0$

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 $a = 6$ , $b = 0$ , and $c = - 19$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (6 \cdot - 19)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 6 \cdot - 19}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 19$ .

Multiply $- 4$ by $6$ .

$x = \frac{0 \pm \sqrt{0 - 24 \cdot - 19}}{2 \cdot 6}$

Multiply $- 24$ by $- 19$ .

$x = \frac{0 \pm \sqrt{0 + 456}}{2 \cdot 6}$

Add $0$ and $456$ .

$x = \frac{0 \pm \sqrt{456}}{2 \cdot 6}$

Rewrite $456$ as $2^{2} \cdot 114$ .

Factor $4$ out of $456$ .

$x = \frac{0 \pm \sqrt{4 (114)}}{2 \cdot 6}$

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

$x = \frac{0 \pm \sqrt{2^{2} \cdot 114}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{0 \pm 2 \sqrt{114}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{0 \pm 2 \sqrt{114}}{12}$

Simplify $\frac{0 \pm 2 \sqrt{114}}{12}$ .

$x = \frac{\pm \sqrt{114}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\pm \sqrt{114}}{6}$

Decimal Form:

$x = 1.77951304 \dots, - 1.77951304 \dots$