Solve 6y^2-2=30

$$6 y ^ { 2 } - 2 = 30$$

Solve for y

$$y = \frac{4 \sqrt{3}}{3} \approx 2.309401077$$

$$y = -\frac{4 \sqrt{3}}{3} \approx -2.309401077$$

Steps by Finding Square Root

Add 2 to both sides.

$$6y^{2}=30+2$$

Add 30 and 2 to get 32.

$$6y^{2}=32$$

Divide both sides by 6.

$$y^{2}=\frac{32}{6}$$

Reduce the fraction \frac{32}{6} to lowest terms by extracting and canceling out 2.

$$y^{2}=\frac{16}{3}$$

Take the square root of both sides of the equation.

$$y=\frac{4\sqrt{3}}{3} y=-\frac{4\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Subtract 30 from both sides.

$$6y^{2}-2-30=0$$

Subtract 30 from -2 to get -32.

$$6y^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 6\left(-32\right)}}{2\times 6}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 6\left(-32\right)}}{2\times 6}$$

Multiply -4 times 6.

$$y=\frac{0±\sqrt{-24\left(-32\right)}}{2\times 6}$$

Multiply -24 times -32.

$$y=\frac{0±\sqrt{768}}{2\times 6}$$

Take the square root of 768.

$$y=\frac{0±16\sqrt{3}}{2\times 6}$$

Multiply 2 times 6.

$$y=\frac{0±16\sqrt{3}}{12}$$

Now solve the equation y=\frac{0±16\sqrt{3}}{12} when ± is plus.

$$y=\frac{4\sqrt{3}}{3}$$

Now solve the equation y=\frac{0±16\sqrt{3}}{12} when ± is minus.

$$y=-\frac{4\sqrt{3}}{3}$$

The equation is now solved.

$$y=\frac{4\sqrt{3}}{3} y=-\frac{4\sqrt{3}}{3}$$