Solve sqrt{8y-3r/4}=2t

$$\sqrt { \frac { 8 y - 3 r } { 4 } } = 2 t$$

Solve for r

$$r=\frac{8\left(y-2t^{2}\right)}{3}$$

$$t\geq 0$$

Steps for Solving Radical Equations

Divide each term of 8y-3r by 4 to get 2y-\frac{3}{4}r.

$$\sqrt{2y-\frac{3}{4}r}=2t$$

Square both sides of the equation.

$$-\frac{3}{4}r+2y=4t^{2}$$

Subtract 2y from both sides of the equation.

$$-\frac{3}{4}r+2y-2y=4t^{2}-2y$$

Subtracting 2y from itself leaves 0.

$$-\frac{3}{4}r=4t^{2}-2y$$

Divide both sides of the equation by -\frac{3}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{4}r}{-\frac{3}{4}}=\frac{4t^{2}-2y}{-\frac{3}{4}}$$

Dividing by -\frac{3}{4} undoes the multiplication by -\frac{3}{4}.

$$r=\frac{4t^{2}-2y}{-\frac{3}{4}}$$

Divide 4t^{2}-2y by -\frac{3}{4} by multiplying 4t^{2}-2y by the reciprocal of -\frac{3}{4}.

$$r=\frac{8y-16t^{2}}{3}$$

Solve for r (complex solution)

$$r=\frac{8\left(y-2t^{2}\right)}{3}$$

$$arg(t)<\pi \text{ or }t=0$$

Solve for t (complex solution)

$$t=\frac{\sqrt{8y-3r}}{4}$$

Solve for t

$$t=\frac{\sqrt{8y-3r}}{4}$$

$$y\geq \frac{3r}{8}$$