X2+(y+4)2=52

Solution for X2+(y+4)2=52 equation:

X2+(X+4)2=52

We move all terms to the left:

X2+(X+4)2-(52)=0

We add all the numbers together, and all the variables

X^2+(X+4)2-52=0

We multiply parentheses

X^2+2X+8-52=0

We add all the numbers together, and all the variables

X^2+2X-44=0

a = 1; b = 2; c = -44;
Δ = b2-4ac
Δ = 22-4·1·(-44)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{5}}{2*1}=\frac{-2-6\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{5}}{2*1}=\frac{-2+6\sqrt{5}}{2}
$