X^2+y^2=17X+4y=0

Solution for X^2+y^2=17X+4y=0 equation:

X^2+X^2=17X+4X=0

We move all terms to the left:

X^2+X^2-(17X+4X)=0

We add all the numbers together, and all the variables

X^2+X^2-(+21X)=0

We add all the numbers together, and all the variables

2X^2-(+21X)=0

We get rid of parentheses

2X^2-21X=0

a = 2; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·2·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*2}=\frac{42}{4}
=10+1/2
$