Solve y^2=-1/30+67/60

$$y ^ { 2 } = - \frac { 1 } { 30 } + 6 \frac { 7 } { 60 }$$

Solve for y

$$y = \frac{\sqrt{219}}{6} \approx 2.466441431$$

$$y = -\frac{\sqrt{219}}{6} \approx -2.466441431$$

Steps by Finding Square Root

Multiply both sides of the equation by 60, the least common multiple of 30,60.

$$60y^{2}=-2+6\times 60+7$$

Multiply 6 and 60 to get 360.

$$60y^{2}=-2+360+7$$

Add -2 and 360 to get 358.

$$60y^{2}=358+7$$

Add 358 and 7 to get 365.

$$60y^{2}=365$$

Divide both sides by 60.

$$y^{2}=\frac{365}{60}$$

Reduce the fraction \frac{365}{60} to lowest terms by extracting and canceling out 5.

$$y^{2}=\frac{73}{12}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{219}}{6} y=-\frac{\sqrt{219}}{6}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 60, the least common multiple of 30,60.

$$60y^{2}=-2+6\times 60+7$$

Multiply 6 and 60 to get 360.

$$60y^{2}=-2+360+7$$

Add -2 and 360 to get 358.

$$60y^{2}=358+7$$

Add 358 and 7 to get 365.

$$60y^{2}=365$$

Subtract 365 from both sides.

$$60y^{2}-365=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 60 for a, 0 for b, and -365 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 60\left(-365\right)}}{2\times 60}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 60\left(-365\right)}}{2\times 60}$$

Multiply -4 times 60.

$$y=\frac{0±\sqrt{-240\left(-365\right)}}{2\times 60}$$

Multiply -240 times -365.

$$y=\frac{0±\sqrt{87600}}{2\times 60}$$

Take the square root of 87600.

$$y=\frac{0±20\sqrt{219}}{2\times 60}$$

Multiply 2 times 60.

$$y=\frac{0±20\sqrt{219}}{120}$$

Now solve the equation y=\frac{0±20\sqrt{219}}{120} when ± is plus.

$$y=\frac{\sqrt{219}}{6}$$

Now solve the equation y=\frac{0±20\sqrt{219}}{120} when ± is minus.

$$y=-\frac{\sqrt{219}}{6}$$

The equation is now solved.

$$y=\frac{\sqrt{219}}{6} y=-\frac{\sqrt{219}}{6}$$