Solve 3/4x^2/2=24

$$\frac { \frac { 3 } { 4 } x ^ { 2 } } { 2 } = 24$$

Solve for x

$$x=8$$

$$x=-8$$

Steps Using Difference of Squares

Multiply both sides by 2.

$$\frac{3}{4}x^{2}=24\times 2$$

Multiply 24 and 2 to get 48.

$$\frac{3}{4}x^{2}=48$$

Subtract 48 from both sides.

$$\frac{3}{4}x^{2}-48=0$$

Divide both sides by \frac{3}{4}.

$$x^{2}-64=0$$

Consider x^{2}-64. Rewrite x^{2}-64 as x^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-8\right)\left(x+8\right)=0$$

To find equation solutions, solve x-8=0 and x+8=0.

$$x=8 x=-8$$

Steps by Finding Square Root

Multiply both sides by 2.

$$\frac{3}{4}x^{2}=24\times 2$$

Multiply 24 and 2 to get 48.

$$\frac{3}{4}x^{2}=48$$

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

$$x^{2}=48\times \frac{4}{3}$$

Multiply 48 and \frac{4}{3} to get 64.

$$x^{2}=64$$

Take the square root of both sides of the equation.

$$x=8 x=-8$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$\frac{3}{4}x^{2}=24\times 2$$

Multiply 24 and 2 to get 48.

$$\frac{3}{4}x^{2}=48$$

Subtract 48 from both sides.

$$\frac{3}{4}x^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{4} for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{4}\left(-48\right)}}{2\times \frac{3}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{4}\left(-48\right)}}{2\times \frac{3}{4}}$$

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

$$x=\frac{0±\sqrt{-3\left(-48\right)}}{2\times \frac{3}{4}}$$

Multiply -3 times -48.

$$x=\frac{0±\sqrt{144}}{2\times \frac{3}{4}}$$

Take the square root of 144.

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

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

$$x=\frac{0±12}{\frac{3}{2}}$$

Now solve the equation x=\frac{0±12}{\frac{3}{2}} when ± is plus. Divide 12 by \frac{3}{2} by multiplying 12 by the reciprocal of \frac{3}{2}.

$$x=8$$

Now solve the equation x=\frac{0±12}{\frac{3}{2}} when ± is minus. Divide -12 by \frac{3}{2} by multiplying -12 by the reciprocal of \frac{3}{2}.

$$x=-8$$

The equation is now solved.

$$x=8 x=-8$$