Question

Solve the given quadratic equation by factorisation method, $\sqrt{5}{x}^2+2x=3\sqrt{5}$

Answer 1

The given quadratic equation $\sqrt{5}{x}^2+2x=3\sqrt{5}$ can be factorised as follows:

$\sqrt{5}{x}^2+2x=3\sqrt{5}\Rightarrow \sqrt{5}{x}^2+2x-3\sqrt{5}=0\Rightarrow \sqrt{5}{x}^2+5x-3x-3\sqrt{5}=0\Rightarrow \sqrt{5}x(x+\sqrt{5})-3(x+\sqrt{5})=0\Rightarrow (\sqrt{5}x-3)=0,(x+\sqrt{5})=0\Rightarrow \sqrt{5}x=3,x=-\sqrt{5}\Rightarrow x=\frac{3}{\sqrt{5}},x=-\sqrt{5}$

Hence, $x=\frac{3}{\sqrt{5}}$ or $x=-\sqrt{5}$