Solve for a
a=10\left(\sqrt{6}-\sqrt{2}\right)\approx 10.352761804
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a\sqrt{2}+a\sqrt{6}=40
Multiply both sides of the equation by 2.
\left(\sqrt{2}+\sqrt{6}\right)a=40
Combine all terms containing a.
\frac{\left(\sqrt{2}+\sqrt{6}\right)a}{\sqrt{2}+\sqrt{6}}=\frac{40}{\sqrt{2}+\sqrt{6}}
Divide both sides by \sqrt{2}+\sqrt{6}.
a=\frac{40}{\sqrt{2}+\sqrt{6}}
Dividing by \sqrt{2}+\sqrt{6} undoes the multiplication by \sqrt{2}+\sqrt{6}.
a=10\sqrt{6}-10\sqrt{2}
Divide 40 by \sqrt{2}+\sqrt{6}.
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