Solve 3t^2-48=0

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

Solve for t

$$t=4$$

$$t=-4$$

Steps Using Difference of Squares

Divide both sides by 3.

$$t^{2}-16=0$$

Consider t^{2}-16. Rewrite t^{2}-16 as t^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(t-4\right)\left(t+4\right)=0$$

To find equation solutions, solve t-4=0 and t+4=0.

$$t=4 t=-4$$

Steps by Finding Square Root

Add 48 to both sides. Anything plus zero gives itself.

$$3t^{2}=48$$

Divide both sides by 3.

$$t^{2}=\frac{48}{3}$$

Divide 48 by 3 to get 16.

$$t^{2}=16$$

Take the square root of both sides of the equation.

$$t=4 t=-4$$

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.

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

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}.

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

Square 0.

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

Multiply -4 times 3.

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

Multiply -12 times -48.

$$t=\frac{0±\sqrt{576}}{2\times 3}$$

Take the square root of 576.

$$t=\frac{0±24}{2\times 3}$$

Multiply 2 times 3.

$$t=\frac{0±24}{6}$$

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

$$t=4$$

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

$$t=-4$$

The equation is now solved.

$$t=4 t=-4$$