Solve 3y^2/2-6=0

$$\frac { 3 y ^ { 2 } } { 2 } - 6 = 0$$

Solve for y

$$y=2$$

$$y=-2$$

Steps Using Difference of Squares

Multiply both sides of the equation by 2.

$$3y^{2}-12=0$$

Divide both sides by 3.

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

Consider y^{2}-4. Rewrite y^{2}-4 as y^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-2\right)\left(y+2\right)=0$$

To find equation solutions, solve y-2=0 and y+2=0.

$$y=2 y=-2$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$3y^{2}-12=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$3y^{2}=12$$

Divide both sides by 3.

$$y^{2}=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$y^{2}=4$$

Take the square root of both sides of the equation.

$$y=2 y=-2$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$3y^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 3\left(-12\right)}}{2\times 3}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 3\left(-12\right)}}{2\times 3}$$

Multiply -4 times 3.

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

Multiply -12 times -12.

$$y=\frac{0±\sqrt{144}}{2\times 3}$$

Take the square root of 144.

$$y=\frac{0±12}{2\times 3}$$

Multiply 2 times 3.

$$y=\frac{0±12}{6}$$

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

$$y=2$$

Now solve the equation y=\frac{0±12}{6} when ± is minus. Divide -12 by 6.

$$y=-2$$

The equation is now solved.

$$y=2 y=-2$$