X^2+y^2=180X-y=-6

Solution for X^2+y^2=180X-y=-6 equation:

X^2+X^2=180X-X=-6

We move all terms to the left:

X^2+X^2-(180X-X)=0

We add all the numbers together, and all the variables

X^2+X^2-(+179X)=0

We add all the numbers together, and all the variables

2X^2-(+179X)=0

We get rid of parentheses

2X^2-179X=0

a = 2; b = -179; c = 0;
Δ = b2-4ac
Δ = -1792-4·2·0
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-179)-179}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+179}{2*2}=\frac{358}{4}
=89+1/2
$