Solve 3y^2quad2=4

$$3 y ^ { 2 } \quad 2 = 4$$

Solve for y

$$y=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$y=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Multiply 3 and 2 to get 6.

$$6y^{2}=4$$

Divide both sides by 6.

$$y^{2}=\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{6}}{3} y=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Multiply 3 and 2 to get 6.

$$6y^{2}=4$$

Subtract 4 from both sides.

$$6y^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 6.

$$y=\frac{0±\sqrt{-24\left(-4\right)}}{2\times 6}$$

Multiply -24 times -4.

$$y=\frac{0±\sqrt{96}}{2\times 6}$$

Take the square root of 96.

$$y=\frac{0±4\sqrt{6}}{2\times 6}$$

Multiply 2 times 6.

$$y=\frac{0±4\sqrt{6}}{12}$$

Now solve the equation y=\frac{0±4\sqrt{6}}{12} when ± is plus.

$$y=\frac{\sqrt{6}}{3}$$

Now solve the equation y=\frac{0±4\sqrt{6}}{12} when ± is minus.

$$y=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$y=\frac{\sqrt{6}}{3} y=-\frac{\sqrt{6}}{3}$$