X2+y2+12y-45=0

Solution for X2+y2+12y-45=0 equation:

X2+X2+12X-45=0

We add all the numbers together, and all the variables

2X^2+12X-45=0

a = 2; b = 12; c = -45;
Δ = b2-4ac
Δ = 122-4·2·(-45)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{14}}{2*2}=\frac{-12-6\sqrt{14}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{14}}{2*2}=\frac{-12+6\sqrt{14}}{4}
$