Solve 3/4x^2-4=0

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

Solve for x

$$x = \frac{4 \sqrt{3}}{3} \approx 2.309401077$$

$$x = -\frac{4 \sqrt{3}}{3} \approx -2.309401077$$

Steps by Finding Square Root

Add 4 to both sides. Anything plus zero gives itself.

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

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

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

Multiply 4 and \frac{4}{3} to get \frac{16}{3}.

$$x^{2}=\frac{16}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{3}}{3} x=-\frac{4\sqrt{3}}{3}$$

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.

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

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

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

Square 0.

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

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

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

Multiply -3 times -4.

$$x=\frac{0±\sqrt{12}}{2\times \frac{3}{4}}$$

Take the square root of 12.

$$x=\frac{0±2\sqrt{3}}{2\times \frac{3}{4}}$$

Multiply 2 times \frac{3}{4}.

$$x=\frac{0±2\sqrt{3}}{\frac{3}{2}}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{\frac{3}{2}} when ± is plus.

$$x=\frac{4\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{\frac{3}{2}} when ± is minus.

$$x=-\frac{4\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{4\sqrt{3}}{3} x=-\frac{4\sqrt{3}}{3}$$