Question

Solve$\frac{3}{4}{y}^2-3=18$.

Short answer

The solutions are$y=2\sqrt{7},y=-2\sqrt{7}$.

Step-by-step solution

Given Information.   

The Given equation is$\frac{3}{4}{y}^2-3=18$.

Isolate the quadratic term and makes its coefficient one.    

$$\begin{gathered} \frac{3}{4}{y}^2-3=18 \\ \frac{3}{4}{y}^2=18+3 \\ \frac{3}{4}{y}^2=21 \end{gathered}$$

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

$$\begin{gathered} y^2=21\times \frac{4}{3} \\ {y}^2=28 \end{gathered}$$

 Use the square root property.   

$y=\pm \sqrt{28}$

Solve radical.

$$\begin{gathered} y=\pm \sqrt{2\times 2\times 7} \\ y=\pm 2\sqrt{7} \end{gathered}$$

Thus, the solutions are$y=2\sqrt{7},y=-2\sqrt{7}$.