Solve h^2=sqrt{5a_{0}}+sqrt{5a}

$$h ^ { 2 } = \sqrt { 5 a _ { 0 } } + \sqrt { 5 a }$$

Solve for a

$$a=\frac{\left(\sqrt{5}h^{2}-5\sqrt{a_{0}}\right)^{2}}{25}$$

$$a_{0}\geq 0\text{ and }\frac{\sqrt{5}h^{2}}{5}-\sqrt{a_{0}}\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{5a_{0}}+\sqrt{5a}=h^{2}$$

Subtract \sqrt{5a_{0}} from both sides.

$$\sqrt{5a}=h^{2}-\sqrt{5a_{0}}$$

Square both sides of the equation.

$$5a=\left(h^{2}-\sqrt{5a_{0}}\right)^{2}$$

Divide both sides by 5.

$$\frac{5a}{5}=\frac{\left(h^{2}-\sqrt{5a_{0}}\right)^{2}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$a=\frac{\left(h^{2}-\sqrt{5a_{0}}\right)^{2}}{5}$$

Solve for a_0

$$a_{0}=\frac{\left(\sqrt{5}h^{2}-5\sqrt{a}\right)^{2}}{25}$$

$$a\geq 0\text{ and }\frac{\sqrt{5}h^{2}}{5}-\sqrt{a}\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{5a_{0}}+\sqrt{5a}=h^{2}$$

Subtract \sqrt{5a} from both sides.

$$\sqrt{5a_{0}}=h^{2}-\sqrt{5a}$$

Square both sides of the equation.

$$5a_{0}=\left(h^{2}-\sqrt{5a}\right)^{2}$$

Divide both sides by 5.

$$\frac{5a_{0}}{5}=\frac{\left(h^{2}-\sqrt{5a}\right)^{2}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$a_{0}=\frac{\left(h^{2}-\sqrt{5a}\right)^{2}}{5}$$