Solve 1/3x^2-3/4=0

$$\frac{ 1 }{ 3 } { x }^{ 2 } - \frac{ 3 }{ 4 } =0$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using Difference of Squares

Multiply both sides by 12.

$$4x^{2}-9=0$$

Consider 4x^{2}-9. Rewrite 4x^{2}-9 as \left(2x\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-3\right)\left(2x+3\right)=0$$

To find equation solutions, solve 2x-3=0 and 2x+3=0.

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

Steps by Finding Square Root

Add \frac{3}{4} to both sides. Anything plus zero gives itself.

$$\frac{1}{3}x^{2}=\frac{3}{4}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

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

Multiply \frac{3}{4} and 3 to get \frac{9}{4}.

$$x^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

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

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.

$$\frac{1}{3}x^{2}-\frac{3}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{3} for a, 0 for b, and -\frac{3}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{3}\left(-\frac{3}{4}\right)}}{2\times \frac{1}{3}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{3}\left(-\frac{3}{4}\right)}}{2\times \frac{1}{3}}$$

Multiply -4 times \frac{1}{3}.

$$x=\frac{0±\sqrt{-\frac{4}{3}\left(-\frac{3}{4}\right)}}{2\times \frac{1}{3}}$$

Multiply -\frac{4}{3} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{1}}{2\times \frac{1}{3}}$$

Take the square root of 1.

$$x=\frac{0±1}{2\times \frac{1}{3}}$$

Multiply 2 times \frac{1}{3}.

$$x=\frac{0±1}{\frac{2}{3}}$$

Now solve the equation x=\frac{0±1}{\frac{2}{3}} when ± is plus. Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.

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

Now solve the equation x=\frac{0±1}{\frac{2}{3}} when ± is minus. Divide -1 by \frac{2}{3} by multiplying -1 by the reciprocal of \frac{2}{3}.

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

The equation is now solved.

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