Solve 5y^2-20=0

$$5 y ^ { 2 } - 20 = 0$$

Solve for y

$$y=2$$

$$y=-2$$

Steps Using Difference of Squares

Divide both sides by 5.

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

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

Add 20 to both sides. Anything plus zero gives itself.

$$5y^{2}=20$$

Divide both sides by 5.

$$y^{2}=\frac{20}{5}$$

Divide 20 by 5 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

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$5y^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 5\left(-20\right)}}{2\times 5}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 5\left(-20\right)}}{2\times 5}$$

Multiply -4 times 5.

$$y=\frac{0±\sqrt{-20\left(-20\right)}}{2\times 5}$$

Multiply -20 times -20.

$$y=\frac{0±\sqrt{400}}{2\times 5}$$

Take the square root of 400.

$$y=\frac{0±20}{2\times 5}$$

Multiply 2 times 5.

$$y=\frac{0±20}{10}$$

Now solve the equation y=\frac{0±20}{10} when ± is plus. Divide 20 by 10.

$$y=2$$

Now solve the equation y=\frac{0±20}{10} when ± is minus. Divide -20 by 10.

$$y=-2$$

The equation is now solved.

$$y=2 y=-2$$