<s>[INST] Solve $y^2 + 3xy - 10x^2 + y + 5x = 0$ for y in terms of x I'm given the following equation: $y^2 + 3xy - 10x^2 + y + 5x = 0$
and asked to solve $y$ in terms of $y$. 
My attempt: 
$y^2 + (3x+1)\times y - 10x^2 + 5x = 0$
$\Rightarrow (y+(3x+1)/2)^2 - ((3x+1)/2)^2  = (x - (\frac 12)\times x)^2 - (\frac 12)^2  $
But I cant seem to get any further and it's probably in the wrong direction. 
 [/INST] $$y^2 + 3xy - 10x^2 + y + 5x = 0\Rightarrow y^2+(3x+1)y-(10x^2-5x) = 0$$
So $$\displaystyle y = \frac{-(3x+1)\pm \sqrt{(3x+1)^2+4(10x^2-5x)}}{2}$$
$$\displaystyle  = \frac{-(3x+1)\pm \sqrt{49x^2-14x+1}}{2}$$
so we get $$\displaystyle y = \frac{-(3x+1)\pm \sqrt{(7x-1)^2}}{3} = \frac{-(3x+1)\pm (7x-1)}{2}$$
So we get $\displaystyle y = 2x-1\;\;,-5x$
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