Solve 150-6x^2=0

$$150-6 { x }^{ 2 } =0$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

Subtract 150 from both sides. Anything subtracted from zero gives its negation.

$$-6x^{2}=-150$$

Divide both sides by -6.

$$x^{2}=\frac{-150}{-6}$$

Divide -150 by -6 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.

$$-6x^{2}+150=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 150 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 150}}{2\left(-6\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)\times 150}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24\times 150}}{2\left(-6\right)}$$

Multiply 24 times 150.

$$x=\frac{0±\sqrt{3600}}{2\left(-6\right)}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{0±60}{-12}$$

Now solve the equation x=\frac{0±60}{-12} when ± is plus. Divide 60 by -12.

$$x=-5$$

Now solve the equation x=\frac{0±60}{-12} when ± is minus. Divide -60 by -12.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$