Solve 8s^2-3=0

$$8 s ^ { 2 } - 3 = 0$$

Solve for s

$$s=\frac{\sqrt{6}}{4}\approx 0.612372436$$

$$s=-\frac{\sqrt{6}}{4}\approx -0.612372436$$

Steps by Finding Square Root

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

$$8s^{2}=3$$

Divide both sides by 8.

$$s^{2}=\frac{3}{8}$$

Take the square root of both sides of the equation.

$$s=\frac{\sqrt{6}}{4} s=-\frac{\sqrt{6}}{4}$$

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.

$$8s^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\times 8\left(-3\right)}}{2\times 8}$$

Square 0.

$$s=\frac{0±\sqrt{-4\times 8\left(-3\right)}}{2\times 8}$$

Multiply -4 times 8.

$$s=\frac{0±\sqrt{-32\left(-3\right)}}{2\times 8}$$

Multiply -32 times -3.

$$s=\frac{0±\sqrt{96}}{2\times 8}$$

Take the square root of 96.

$$s=\frac{0±4\sqrt{6}}{2\times 8}$$

Multiply 2 times 8.

$$s=\frac{0±4\sqrt{6}}{16}$$

Now solve the equation s=\frac{0±4\sqrt{6}}{16} when ± is plus.

$$s=\frac{\sqrt{6}}{4}$$

Now solve the equation s=\frac{0±4\sqrt{6}}{16} when ± is minus.

$$s=-\frac{\sqrt{6}}{4}$$

The equation is now solved.

$$s=\frac{\sqrt{6}}{4} s=-\frac{\sqrt{6}}{4}$$