Solve 5s^2-3=0

$$5 s ^ { 2 } - 3 = 0$$

Solve for s

$$s=\frac{\sqrt{15}}{5}\approx 0.774596669$$

$$s=-\frac{\sqrt{15}}{5}\approx -0.774596669$$

Steps by Finding Square Root

Add 3 to both sides. Anything plus zero gives itself.

$$5s^{2}=3$$

Divide both sides by 5.

$$s^{2}=\frac{3}{5}$$

Take the square root of both sides of the equation.

$$s=\frac{\sqrt{15}}{5} s=-\frac{\sqrt{15}}{5}$$

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.

$$5s^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\times 5\left(-3\right)}}{2\times 5}$$

Square 0.

$$s=\frac{0±\sqrt{-4\times 5\left(-3\right)}}{2\times 5}$$

Multiply -4 times 5.

$$s=\frac{0±\sqrt{-20\left(-3\right)}}{2\times 5}$$

Multiply -20 times -3.

$$s=\frac{0±\sqrt{60}}{2\times 5}$$

Take the square root of 60.

$$s=\frac{0±2\sqrt{15}}{2\times 5}$$

Multiply 2 times 5.

$$s=\frac{0±2\sqrt{15}}{10}$$

Now solve the equation s=\frac{0±2\sqrt{15}}{10} when ± is plus.

$$s=\frac{\sqrt{15}}{5}$$

Now solve the equation s=\frac{0±2\sqrt{15}}{10} when ± is minus.

$$s=-\frac{\sqrt{15}}{5}$$

The equation is now solved.

$$s=\frac{\sqrt{15}}{5} s=-\frac{\sqrt{15}}{5}$$