Solve c=3b^2-2a/5

$$c = \frac { 3 b ^ { 2 } - 2 a } { 5 }$$

Solve for a

$$a=\frac{3b^{2}-5c}{2}$$

Steps for Solving Linear Equation

Divide each term of 3b^{2}-2a by 5 to get \frac{3}{5}b^{2}-\frac{2}{5}a.

$$c=\frac{3}{5}b^{2}-\frac{2}{5}a$$

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

$$\frac{3}{5}b^{2}-\frac{2}{5}a=c$$

Subtract \frac{3}{5}b^{2} from both sides.

$$-\frac{2}{5}a=c-\frac{3}{5}b^{2}$$

The equation is in standard form.

$$-\frac{2}{5}a=-\frac{3b^{2}}{5}+c$$

Divide both sides of the equation by -\frac{2}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{2}{5}a}{-\frac{2}{5}}=\frac{-\frac{3b^{2}}{5}+c}{-\frac{2}{5}}$$

Dividing by -\frac{2}{5} undoes the multiplication by -\frac{2}{5}.

$$a=\frac{-\frac{3b^{2}}{5}+c}{-\frac{2}{5}}$$

Divide c-\frac{3b^{2}}{5} by -\frac{2}{5} by multiplying c-\frac{3b^{2}}{5} by the reciprocal of -\frac{2}{5}.

$$a=\frac{3b^{2}-5c}{2}$$

Solve for b

$$b=\frac{\sqrt{6a+15c}}{3}$$

$$b=-\frac{\sqrt{6a+15c}}{3}\text{, }c\geq -\frac{2a}{5}$$