Solve 10=3t^2/12

$$10 = 3 t ^ { 2 } / 12$$

Solve for t

$$t=2\sqrt{10}\approx 6.32455532$$

$$t=-2\sqrt{10}\approx -6.32455532$$

Steps by Finding Square Root

Multiply both sides by 12.

$$10\times 12=3t^{2}$$

Multiply 10 and 12 to get 120.

$$120=3t^{2}$$

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

$$3t^{2}=120$$

Divide both sides by 3.

$$t^{2}=\frac{120}{3}$$

Divide 120 by 3 to get 40.

$$t^{2}=40$$

Take the square root of both sides of the equation.

$$t=2\sqrt{10} t=-2\sqrt{10}$$

Steps Using the Quadratic Formula

Multiply both sides by 12.

$$10\times 12=3t^{2}$$

Multiply 10 and 12 to get 120.

$$120=3t^{2}$$

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

$$3t^{2}=120$$

Subtract 120 from both sides.

$$3t^{2}-120=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -120 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 3\left(-120\right)}}{2\times 3}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 3\left(-120\right)}}{2\times 3}$$

Multiply -4 times 3.

$$t=\frac{0±\sqrt{-12\left(-120\right)}}{2\times 3}$$

Multiply -12 times -120.

$$t=\frac{0±\sqrt{1440}}{2\times 3}$$

Take the square root of 1440.

$$t=\frac{0±12\sqrt{10}}{2\times 3}$$

Multiply 2 times 3.

$$t=\frac{0±12\sqrt{10}}{6}$$

Now solve the equation t=\frac{0±12\sqrt{10}}{6} when ± is plus.

$$t=2\sqrt{10}$$

Now solve the equation t=\frac{0±12\sqrt{10}}{6} when ± is minus.

$$t=-2\sqrt{10}$$

The equation is now solved.

$$t=2\sqrt{10} t=-2\sqrt{10}$$