problem with quadratic equation two variable

Question

I have following equation $a^2+4.8ab-b^2=0$ and I have problem with solving it, I don't know why $a=-5 $ or $ a=0.2 $

Answer 1

If you multiply the equation by $5$ to get $5a^2+24ab-5b^2=0$ then you have the solution $a=b=0$, or you can divide throughout by $b^2$ and set $x=\frac ab$ which gives you $$5x^2+24x-5=0=(5x-1)(x+5)$$ so $a=-5b$ or $a=\frac b5$

With a homogeneous form like this, you need a homogeneous solution. I've left a few gaps for you to fill.

Answer 2

Divide both sides through $b^2$, for instance, and let $x=\frac ab$ . Then solve for x.