Solve 6x^2+7=85

$$6 { x }^{ 2 } +7=85$$

Solve for x

$$x=\sqrt{13}\approx 3.605551275$$

$$x=-\sqrt{13}\approx -3.605551275$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$6x^{2}=85-7$$

Subtract 7 from 85 to get 78.

$$6x^{2}=78$$

Divide both sides by 6.

$$x^{2}=\frac{78}{6}$$

Divide 78 by 6 to get 13.

$$x^{2}=13$$

Take the square root of both sides of the equation.

$$x=\sqrt{13} x=-\sqrt{13}$$

Steps Using the Quadratic Formula

Subtract 85 from both sides.

$$6x^{2}+7-85=0$$

Subtract 85 from 7 to get -78.

$$6x^{2}-78=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -78 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-78\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-78\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-78\right)}}{2\times 6}$$

Multiply -24 times -78.

$$x=\frac{0±\sqrt{1872}}{2\times 6}$$

Take the square root of 1872.

$$x=\frac{0±12\sqrt{13}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±12\sqrt{13}}{12}$$

Now solve the equation x=\frac{0±12\sqrt{13}}{12} when ± is plus.

$$x=\sqrt{13}$$

Now solve the equation x=\frac{0±12\sqrt{13}}{12} when ± is minus.

$$x=-\sqrt{13}$$

The equation is now solved.

$$x=\sqrt{13} x=-\sqrt{13}$$