Find expressions, in terms of m and n, for the roots of the equation: (3m-x)÷(x+n)=2(x+m)÷(x-n)
$\frac{3m-x}{x+n} = $$\frac{2(x+m)}{x-n}$
Answer: $\frac{-(n-m)±\sqrt{\mathstrut (n-m)^2-60nm}} 2$
I tried doing it like an almost identical question before, but the method is not working for this question or I'm doing it wrong. my answers keep being some version of this:
$-3x^2-x(n-m)+mn$ Then I tried to use the quadratic formula on it, but it never got to the answer I wanted.
You simplified incorrectly. It should be:
$$(3m-x)(x-n) = 2(x+n)(x+m)$$ $$3mx-3mn-x^2+xn = 2x^2+2mx+2xn+2mn$$ $$-3x^2+mx-nx-\color{red}{5mn}=0$$