Solve 0=3x^2-7

$$0=3 { x }^{ 2 } -7$$

Solve for x

$$x = \frac{\sqrt{21}}{3} \approx 1.527525232$$

$$x = -\frac{\sqrt{21}}{3} \approx -1.527525232$$

Steps by Finding Square Root

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

$$3x^{2}-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$3x^{2}=7$$

Divide both sides by 3.

$$x^{2}=\frac{7}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{21}}{3} x=-\frac{\sqrt{21}}{3}$$

Steps Using the Quadratic Formula

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

$$3x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-7\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-7\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-7\right)}}{2\times 3}$$

Multiply -12 times -7.

$$x=\frac{0±\sqrt{84}}{2\times 3}$$

Take the square root of 84.

$$x=\frac{0±2\sqrt{21}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{21}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{6} when ± is plus.

$$x=\frac{\sqrt{21}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{6} when ± is minus.

$$x=-\frac{\sqrt{21}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{21}}{3} x=-\frac{\sqrt{21}}{3}$$