System of nonlinear equations that leads to cubic equation 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.

The roots are all real:
$x_{1}=-\frac{14}{15}-\frac{\sqrt{4429}.cos\Big(\frac{acot(-f)}{3}\Big)} {15}$,
$x_{2}=-\frac{14}{15}+\frac{\sqrt{4429}.sin\Big(\frac{atan(f)}{3}+\frac{\pi}{3}\Big)} {15}$
$x_{3}=-\frac{14}{15}-\frac{\sqrt{4429}.sin\Big(\frac{atan(f)}{3}\Big)} {15}$
$f=\frac{192158\sqrt{222021105}}{3330316575}$.
