Solve 6x^2+1=8

$$6 x ^ { 2 } + 1 = 8$$

Solve for x

$$x = \frac{\sqrt{42}}{6} \approx 1.08012345$$

$$x = -\frac{\sqrt{42}}{6} \approx -1.08012345$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$6x^{2}=8-1$$

Subtract 1 from 8 to get 7.

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

Divide both sides by 6.

$$x^{2}=\frac{7}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{42}}{6} x=-\frac{\sqrt{42}}{6}$$

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$6x^{2}+1-8=0$$

Subtract 8 from 1 to get -7.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-7\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-7\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-7\right)}}{2\times 6}$$

Multiply -24 times -7.

$$x=\frac{0±\sqrt{168}}{2\times 6}$$

Take the square root of 168.

$$x=\frac{0±2\sqrt{42}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{42}}{12}$$

Now solve the equation x=\frac{0±2\sqrt{42}}{12} when ± is plus.

$$x=\frac{\sqrt{42}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{42}}{12} when ± is minus.

$$x=-\frac{\sqrt{42}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{42}}{6} x=-\frac{\sqrt{42}}{6}$$