X^2+y^2+3y=36

Solution for X^2+y^2+3y=36 equation:

X^2+X^2+3X=36

We move all terms to the left:

X^2+X^2+3X-(36)=0

We add all the numbers together, and all the variables

2X^2+3X-36=0

a = 2; b = 3; c = -36;
Δ = b2-4ac
Δ = 32-4·2·(-36)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{33}}{2*2}=\frac{-3-3\sqrt{33}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{33}}{2*2}=\frac{-3+3\sqrt{33}}{4}
$