Solve 3=1/29.8y^2

$$3= \frac{ 1 }{ 2 } 9.8 { y }^{ 2 }$$

Solve for y

$$y=\frac{\sqrt{30}}{7}\approx 0.782460796$$

$$y=-\frac{\sqrt{30}}{7}\approx -0.782460796$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$3=\frac{49}{10}y^{2}$$

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

$$\frac{49}{10}y^{2}=3$$

Multiply both sides by \frac{10}{49}, the reciprocal of \frac{49}{10}.

$$y^{2}=3\times \frac{10}{49}$$

Multiply 3 and \frac{10}{49} to get \frac{30}{49}.

$$y^{2}=\frac{30}{49}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{30}}{7} y=-\frac{\sqrt{30}}{7}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$3=\frac{49}{10}y^{2}$$

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

$$\frac{49}{10}y^{2}=3$$

Subtract 3 from both sides.

$$\frac{49}{10}y^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{49}{10} for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-3\right)}}{2\times \frac{49}{10}}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-3\right)}}{2\times \frac{49}{10}}$$

Multiply -4 times \frac{49}{10}.

$$y=\frac{0±\sqrt{-\frac{98}{5}\left(-3\right)}}{2\times \frac{49}{10}}$$

Multiply -\frac{98}{5} times -3.

$$y=\frac{0±\sqrt{\frac{294}{5}}}{2\times \frac{49}{10}}$$

Take the square root of \frac{294}{5}.

$$y=\frac{0±\frac{7\sqrt{30}}{5}}{2\times \frac{49}{10}}$$

Multiply 2 times \frac{49}{10}.

$$y=\frac{0±\frac{7\sqrt{30}}{5}}{\frac{49}{5}}$$

Now solve the equation y=\frac{0±\frac{7\sqrt{30}}{5}}{\frac{49}{5}} when ± is plus.

$$y=\frac{\sqrt{30}}{7}$$

Now solve the equation y=\frac{0±\frac{7\sqrt{30}}{5}}{\frac{49}{5}} when ± is minus.

$$y=-\frac{\sqrt{30}}{7}$$

The equation is now solved.

$$y=\frac{\sqrt{30}}{7} y=-\frac{\sqrt{30}}{7}$$