X2-24y+y2=4

Solution for X2-24y+y2=4 equation:

X2-24X+X2=4

We move all terms to the left:

X2-24X+X2-(4)=0

We add all the numbers together, and all the variables

2X^2-24X-4=0

a = 2; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·2·(-4)
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{38}}{2*2}=\frac{24-4\sqrt{38}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{38}}{2*2}=\frac{24+4\sqrt{38}}{4}
$