Solve -3x^2+75=0

$$- 3 x ^ { 2 } + 75 = 0$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

Subtract 75 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-75$$

Divide both sides by -3.

$$x^{2}=\frac{-75}{-3}$$

Divide -75 by -3 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-3x^{2}+75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 75}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 75}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 75}}{2\left(-3\right)}$$

Multiply 12 times 75.

$$x=\frac{0±\sqrt{900}}{2\left(-3\right)}$$

Take the square root of 900.

$$x=\frac{0±30}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±30}{-6}$$

Now solve the equation x=\frac{0±30}{-6} when ± is plus. Divide 30 by -6.

$$x=-5$$

Now solve the equation x=\frac{0±30}{-6} when ± is minus. Divide -30 by -6.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$