Solve x^2-x^2/4=60

$$x ^ { 2 } - \frac { x ^ { 2 } } { 4 } = 60$$

Solve for x

$$x=4\sqrt{5}\approx 8.94427191$$

$$x=-4\sqrt{5}\approx -8.94427191$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$4x^{2}-x^{2}=240$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}=240$$

Divide both sides by 3.

$$x^{2}=\frac{240}{3}$$

Divide 240 by 3 to get 80.

$$x^{2}=80$$

Take the square root of both sides of the equation.

$$x=4\sqrt{5} x=-4\sqrt{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$4x^{2}-x^{2}=240$$

Subtract 240 from both sides.

$$4x^{2}-x^{2}-240=0$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-240\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-240\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-240\right)}}{2\times 3}$$

Multiply -12 times -240.

$$x=\frac{0±\sqrt{2880}}{2\times 3}$$

Take the square root of 2880.

$$x=\frac{0±24\sqrt{5}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±24\sqrt{5}}{6}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{6} when ± is plus.

$$x=4\sqrt{5}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{6} when ± is minus.

$$x=-4\sqrt{5}$$

The equation is now solved.

$$x=4\sqrt{5} x=-4\sqrt{5}$$