Solve sqrt{5}-a=4(1+2bsqrt{5})

$$\sqrt { 5 } - a = 4 ( 1 + 2 b \sqrt { 5 } )$$

Solve for a

$$a=-8\sqrt{5}b+\sqrt{5}-4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by 1+2b\sqrt{5}.

$$\sqrt{5}-a=4+8\sqrt{5}b$$

Subtract \sqrt{5} from both sides.

$$-a=4+8\sqrt{5}b-\sqrt{5}$$

The equation is in standard form.

$$-a=8\sqrt{5}b+4-\sqrt{5}$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{8\sqrt{5}b+4-\sqrt{5}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{8\sqrt{5}b+4-\sqrt{5}}{-1}$$

Divide 4+8\sqrt{5}b-\sqrt{5} by -1.

$$a=-8\sqrt{5}b+\sqrt{5}-4$$

Solve for b

$$b=-\frac{\sqrt{5}\left(a+4-\sqrt{5}\right)}{40}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by 1+2b\sqrt{5}.

$$\sqrt{5}-a=4+8\sqrt{5}b$$

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

$$4+8\sqrt{5}b=\sqrt{5}-a$$

Subtract 4 from both sides.

$$8\sqrt{5}b=\sqrt{5}-a-4$$

The equation is in standard form.

$$8\sqrt{5}b=-a+\sqrt{5}-4$$

Divide both sides by 8\sqrt{5}.

$$\frac{8\sqrt{5}b}{8\sqrt{5}}=\frac{-a+\sqrt{5}-4}{8\sqrt{5}}$$

Dividing by 8\sqrt{5} undoes the multiplication by 8\sqrt{5}.

$$b=\frac{-a+\sqrt{5}-4}{8\sqrt{5}}$$

Divide \sqrt{5}-a-4 by 8\sqrt{5}.

$$b=\frac{\sqrt{5}\left(-a+\sqrt{5}-4\right)}{40}$$