Solve sqrt{30+6sqrt{5}}*sqrt{60-24sqrt{5}}=3sqrt{5}*x

$$\sqrt{ 30+6 \sqrt{ 5 } } \times \sqrt{ 60-24 \sqrt{ 5 } } =3 \sqrt{ 5 } \times x$$

Solve for x

$$x=2\left(\sqrt{5}-1\right)\approx 2.472135955$$

Steps for Solving Linear Equation

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

$$3\sqrt{5}x=\sqrt{30+6\sqrt{5}}\sqrt{60-24\sqrt{5}}$$

The equation is in standard form.

$$3\sqrt{5}x=\sqrt{60-24\sqrt{5}}\sqrt{6\sqrt{5}+30}$$

Divide both sides by 3\sqrt{5}.

$$\frac{3\sqrt{5}x}{3\sqrt{5}}=\frac{30-6\sqrt{5}}{3\sqrt{5}}$$

Dividing by 3\sqrt{5} undoes the multiplication by 3\sqrt{5}.

$$x=\frac{30-6\sqrt{5}}{3\sqrt{5}}$$

Divide 30-6\sqrt{5} by 3\sqrt{5}.

$$x=2\sqrt{5}-2$$