$$2a=4b+ \sqrt{ 5 }$$
$a=\frac{4b+\sqrt{5}}{2}$
$$2a=4b+\sqrt{5}$$
$$\frac{2a}{2}=\frac{4b+\sqrt{5}}{2}$$
$$a=\frac{4b+\sqrt{5}}{2}$$
$$a=2b+\frac{\sqrt{5}}{2}$$
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$b=\frac{a}{2}-\frac{\sqrt{5}}{4}$
$$4b+\sqrt{5}=2a$$
$$4b=2a-\sqrt{5}$$
$$\frac{4b}{4}=\frac{2a-\sqrt{5}}{4}$$
$$b=\frac{2a-\sqrt{5}}{4}$$
$$b=\frac{a}{2}-\frac{\sqrt{5}}{4}$$
