Solve 6/2x^22=2

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

Solve for x

$$x=\frac{\sqrt{3}}{2}\approx 0.866025404$$

$$x=-\frac{\sqrt{3}}{2}\approx -0.866025404$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x^{2}.

$$6=8x^{2}$$

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

$$8x^{2}=6$$

Divide both sides by 8.

$$x^{2}=\frac{6}{8}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{3}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{2} x=-\frac{\sqrt{3}}{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x^{2}.

$$6=8x^{2}$$

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

$$8x^{2}=6$$

Subtract 6 from both sides.

$$8x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-6\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-6\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-6\right)}}{2\times 8}$$

Multiply -32 times -6.

$$x=\frac{0±\sqrt{192}}{2\times 8}$$

Take the square root of 192.

$$x=\frac{0±8\sqrt{3}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±8\sqrt{3}}{16}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{16} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{3}}{16} when ± is minus.

$$x=-\frac{\sqrt{3}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{2} x=-\frac{\sqrt{3}}{2}$$