Question

Solve the following quadratic equations by factorization:
$3\sqrt{5}{x}^2+25x-10\sqrt{5}=0$

Answer 1

Consider the equation $3\sqrt{5}{x}^2+25x-10\sqrt{5}=0$
$$\begin{gathered} \Rightarrow 3\sqrt{5}{x}^2+30x-5x-10\sqrt{5}=0 \\ \Rightarrow 3\sqrt{5}x\left(x+2\sqrt{5}\right)-5\left(x+2\sqrt{5}\right)=0 \\ \Rightarrow \left(3\sqrt{5}x-5\right)\left(x+2\sqrt{5}\right)=0 \\ \Rightarrow \left(3\sqrt{5}x-5\right)=0\mathrm{or}\left(x+2\sqrt{5}\right)=0 \\ \Rightarrow x=\frac{\sqrt{5}}{3}\mathrm{or}x=-2\sqrt{5} \end{gathered}$$