Solve for x
x = \frac{\sqrt{5} {(\sqrt{10} + 1)}}{9} \approx 1.034126199
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\sqrt{5}+x-\sqrt{10}x=0
Subtract \sqrt{10}x from both sides.
x-\sqrt{10}x=-\sqrt{5}
Subtract \sqrt{5} from both sides. Anything subtracted from zero gives its negation.
\left(1-\sqrt{10}\right)x=-\sqrt{5}
Combine all terms containing x.
\frac{\left(1-\sqrt{10}\right)x}{1-\sqrt{10}}=-\frac{\sqrt{5}}{1-\sqrt{10}}
Divide both sides by 1-\sqrt{10}.
x=-\frac{\sqrt{5}}{1-\sqrt{10}}
Dividing by 1-\sqrt{10} undoes the multiplication by 1-\sqrt{10}.
x=\frac{\sqrt{5}+5\sqrt{2}}{9}
Divide -\sqrt{5} by 1-\sqrt{10}.
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