Question

Solve: $3x^2+2\sqrt{5}x-5=0.$

Answer 1

$$\begin{gathered} \text{3}{x}^2+2\sqrt{5}x-5=0 \\ \text{⇒ 3}{x}^2+3\sqrt{5}x-\sqrt{5}x-5=0 \\ \text{⇒ 3}x(x+\sqrt{5})-\sqrt{5}(x+\sqrt{5})=0 \\ \text{⇒}(x+\sqrt{5})(\text{3}x-\sqrt{5})=0 \\ \therefore x=-\sqrt{5},x=\frac{\sqrt{5}}{3} \end{gathered}$$