Solve P=sqrt{3a+2/2}

$$P = \sqrt { \frac { 3 a + 2 } { 2 } }$$

Solve for a

$$a=\frac{2\left(P^{2}-1\right)}{3}$$

$$P\geq 0$$

Steps for Solving Radical Equations

Divide each term of 3a+2 by 2 to get \frac{3}{2}a+1.

$$P=\sqrt{\frac{3}{2}a+1}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{\frac{3}{2}a+1}=P$$

Square both sides of the equation.

$$\frac{3}{2}a+1=P^{2}$$

Subtract 1 from both sides of the equation.

$$\frac{3}{2}a+1-1=P^{2}-1$$

Subtracting 1 from itself leaves 0.

$$\frac{3}{2}a=P^{2}-1$$

Divide both sides of the equation by \frac{3}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{2}a}{\frac{3}{2}}=\frac{P^{2}-1}{\frac{3}{2}}$$

Dividing by \frac{3}{2} undoes the multiplication by \frac{3}{2}.

$$a=\frac{P^{2}-1}{\frac{3}{2}}$$

Divide P^{2}-1 by \frac{3}{2} by multiplying P^{2}-1 by the reciprocal of \frac{3}{2}.

$$a=\frac{2P^{2}-2}{3}$$

Solve for P

$$P=\frac{\sqrt{6a+4}}{2}$$

$$a\geq -\frac{2}{3}$$