Solve 780x^2=124200

$$780 x ^ { 2 } = 124200$$

Solve for x

$$x = \frac{3 \sqrt{2990}}{13} \approx 12.61866749$$

$$x = -\frac{3 \sqrt{2990}}{13} \approx -12.61866749$$

Steps by Finding Square Root

Divide both sides by 780.

$$x^{2}=\frac{124200}{780}$$

Reduce the fraction \frac{124200}{780} to lowest terms by extracting and canceling out 60.

$$x^{2}=\frac{2070}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{2990}}{13} x=-\frac{3\sqrt{2990}}{13}$$

Steps Using the Quadratic Formula

Divide both sides by 780.

$$x^{2}=\frac{124200}{780}$$

Reduce the fraction \frac{124200}{780} to lowest terms by extracting and canceling out 60.

$$x^{2}=\frac{2070}{13}$$

Subtract \frac{2070}{13} from both sides.

$$x^{2}-\frac{2070}{13}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{2070}{13} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{2070}{13}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{2070}{13}\right)}}{2}$$

Multiply -4 times -\frac{2070}{13}.

$$x=\frac{0±\sqrt{\frac{8280}{13}}}{2}$$

Take the square root of \frac{8280}{13}.

$$x=\frac{0±\frac{6\sqrt{2990}}{13}}{2}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{2990}}{13}}{2} when ± is plus.

$$x=\frac{3\sqrt{2990}}{13}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{2990}}{13}}{2} when ± is minus.

$$x=-\frac{3\sqrt{2990}}{13}$$

The equation is now solved.

$$x=\frac{3\sqrt{2990}}{13} x=-\frac{3\sqrt{2990}}{13}$$