Solve 2+3x^2=4

$$2 + 3 x ^ { 2 } = 4$$

Solve for x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$3x^{2}=4-2$$

Subtract 2 from 4 to get 2.

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

Divide both sides by 3.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract 4 from both sides.

$$2+3x^{2}-4=0$$

Subtract 4 from 2 to get -2.

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

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.

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

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

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

Square 0.

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

Multiply -4 times 3.

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

Multiply -12 times -2.

$$x=\frac{0±\sqrt{24}}{2\times 3}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{6}}{6}$$

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

$$x=\frac{\sqrt{6}}{3}$$

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

$$x=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$