The system of equations are:
$$\begin{align}2x + 3y &= 6 + 5x\\x^2 – 2y^2 – (3x/4y) + 6xy &= 60\end{align}$$
I can solve it through substitution but it is an arduous process to reach this cubic equation:
$$20x^3 + 56x^2 – 243x – 544 = 0$$
And I can only solve this using a computer.
Is there a simpler method?
edit: turns out there was a printing error that made the problem much harder. I posted the actual problem below if you want to see it.
edit 2: The actual problem is far less interesting, but I included it for completeness. There are some really great answers to the above "incorrect" problem however that are definitely worth a read. Thanks everyone for contributing.
Best Answer
Wolfram gives two complex and one real root: $$x=\frac{1}{30}(-28 - \frac{2861}{\sqrt[3]{{498338}+75\sqrt{48312705}}}+\sqrt[3]{{498338}+75\sqrt{48312705}}),$$ which shows that there is no easy way, but following the Cardano method.