Solve 9/4x^2-2/3=0

$$\frac { 9 } { 4 } x ^ { 2 } - \frac { 2 } { 3 } = 0$$

Solve for x

$$x=\frac{2\sqrt{6}}{9}\approx 0.544331054$$

$$x=-\frac{2\sqrt{6}}{9}\approx -0.544331054$$

Steps by Finding Square Root

Add \frac{2}{3} to both sides. Anything plus zero gives itself.

$$\frac{9}{4}x^{2}=\frac{2}{3}$$

Multiply both sides by \frac{4}{9}, the reciprocal of \frac{9}{4}.

$$x^{2}=\frac{2}{3}\times \frac{4}{9}$$

Multiply \frac{2}{3} and \frac{4}{9} to get \frac{8}{27}.

$$x^{2}=\frac{8}{27}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{6}}{9} x=-\frac{2\sqrt{6}}{9}$$

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.

$$\frac{9}{4}x^{2}-\frac{2}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{9}{4} for a, 0 for b, and -\frac{2}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{9}{4}\left(-\frac{2}{3}\right)}}{2\times \frac{9}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{9}{4}\left(-\frac{2}{3}\right)}}{2\times \frac{9}{4}}$$

Multiply -4 times \frac{9}{4}.

$$x=\frac{0±\sqrt{-9\left(-\frac{2}{3}\right)}}{2\times \frac{9}{4}}$$

Multiply -9 times -\frac{2}{3}.

$$x=\frac{0±\sqrt{6}}{2\times \frac{9}{4}}$$

Multiply 2 times \frac{9}{4}.

$$x=\frac{0±\sqrt{6}}{\frac{9}{2}}$$

Now solve the equation x=\frac{0±\sqrt{6}}{\frac{9}{2}} when ± is plus.

$$x=\frac{2\sqrt{6}}{9}$$

Now solve the equation x=\frac{0±\sqrt{6}}{\frac{9}{2}} when ± is minus.

$$x=-\frac{2\sqrt{6}}{9}$$

The equation is now solved.

$$x=\frac{2\sqrt{6}}{9} x=-\frac{2\sqrt{6}}{9}$$