Solve 0=5w^2-90

$$0 = 5 w ^ { 2 } - 90$$

Solve for w

$$w=3\sqrt{2}\approx 4.242640687$$

$$w=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$5w^{2}-90=0$$

Add 90 to both sides. Anything plus zero gives itself.

$$5w^{2}=90$$

Divide both sides by 5.

$$w^{2}=\frac{90}{5}$$

Divide 90 by 5 to get 18.

$$w^{2}=18$$

Take the square root of both sides of the equation.

$$w=3\sqrt{2} w=-3\sqrt{2}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$5w^{2}-90=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -90 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 5\left(-90\right)}}{2\times 5}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 5\left(-90\right)}}{2\times 5}$$

Multiply -4 times 5.

$$w=\frac{0±\sqrt{-20\left(-90\right)}}{2\times 5}$$

Multiply -20 times -90.

$$w=\frac{0±\sqrt{1800}}{2\times 5}$$

Take the square root of 1800.

$$w=\frac{0±30\sqrt{2}}{2\times 5}$$

Multiply 2 times 5.

$$w=\frac{0±30\sqrt{2}}{10}$$

Now solve the equation w=\frac{0±30\sqrt{2}}{10} when ± is plus.

$$w=3\sqrt{2}$$

Now solve the equation w=\frac{0±30\sqrt{2}}{10} when ± is minus.

$$w=-3\sqrt{2}$$

The equation is now solved.

$$w=3\sqrt{2} w=-3\sqrt{2}$$