X^2+Y^2+13y=y-32

Solution for X^2+Y^2+13y=y-32 equation:

X^2+^2+13X=X-32

We move all terms to the left:

X^2+^2+13X-(X-32)=0

We add all the numbers together, and all the variables

X^2+13X-(X-32)=0

We get rid of parentheses

X^2+13X-X+32=0

We add all the numbers together, and all the variables

X^2+12X+32=0

a = 1; b = 12; c = +32;
Δ = b2-4ac
Δ = 122-4·1·32
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4}{2*1}=\frac{-8}{2}
=-4
$