Solve 6x^2-5=0

$$6 x ^ { 2 } - 5 = 0$$

Solve for x

$$x=\frac{\sqrt{30}}{6}\approx 0.912870929$$

$$x=-\frac{\sqrt{30}}{6}\approx -0.912870929$$

Steps by Finding Square Root

Add 5 to both sides. Anything plus zero gives itself.

$$6x^{2}=5$$

Divide both sides by 6.

$$x^{2}=\frac{5}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{6} x=-\frac{\sqrt{30}}{6}$$

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.

$$6x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-5\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-5\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-5\right)}}{2\times 6}$$

Multiply -24 times -5.

$$x=\frac{0±\sqrt{120}}{2\times 6}$$

Take the square root of 120.

$$x=\frac{0±2\sqrt{30}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{30}}{12}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{12} when ± is plus.

$$x=\frac{\sqrt{30}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{12} when ± is minus.

$$x=-\frac{\sqrt{30}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{6} x=-\frac{\sqrt{30}}{6}$$