Solve 0=48-3x^2

$$0=48-3 { x }^{ 2 }$$

Solve for x

$$x=4$$

$$x=-4$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$48-3x^{2}=0$$

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-48$$

Divide both sides by -3.

$$x^{2}=\frac{-48}{-3}$$

Divide -48 by -3 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$48-3x^{2}=0$$

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.

$$-3x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 48}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 48}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 48}}{2\left(-3\right)}$$

Multiply 12 times 48.

$$x=\frac{0±\sqrt{576}}{2\left(-3\right)}$$

Take the square root of 576.

$$x=\frac{0±24}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±24}{-6}$$

Now solve the equation x=\frac{0±24}{-6} when ± is plus. Divide 24 by -6.

$$x=-4$$

Now solve the equation x=\frac{0±24}{-6} when ± is minus. Divide -24 by -6.

$$x=4$$

The equation is now solved.

$$x=-4 x=4$$