Solve 3t^2=38*5

$$3 t ^ { 2 } = 38 \times 5$$

Solve for t

$$t = \frac{\sqrt{570}}{3} \approx 7.958224258$$

$$t = -\frac{\sqrt{570}}{3} \approx -7.958224258$$

Steps by Finding Square Root

Multiply 38 and 5 to get 190.

$$3t^{2}=190$$

Divide both sides by 3.

$$t^{2}=\frac{190}{3}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{570}}{3} t=-\frac{\sqrt{570}}{3}$$

Steps Using the Quadratic Formula

Multiply 38 and 5 to get 190.

$$3t^{2}=190$$

Subtract 190 from both sides.

$$3t^{2}-190=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -190 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 3\left(-190\right)}}{2\times 3}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 3\left(-190\right)}}{2\times 3}$$

Multiply -4 times 3.

$$t=\frac{0±\sqrt{-12\left(-190\right)}}{2\times 3}$$

Multiply -12 times -190.

$$t=\frac{0±\sqrt{2280}}{2\times 3}$$

Take the square root of 2280.

$$t=\frac{0±2\sqrt{570}}{2\times 3}$$

Multiply 2 times 3.

$$t=\frac{0±2\sqrt{570}}{6}$$

Now solve the equation t=\frac{0±2\sqrt{570}}{6} when ± is plus.

$$t=\frac{\sqrt{570}}{3}$$

Now solve the equation t=\frac{0±2\sqrt{570}}{6} when ± is minus.

$$t=-\frac{\sqrt{570}}{3}$$

The equation is now solved.

$$t=\frac{\sqrt{570}}{3} t=-\frac{\sqrt{570}}{3}$$