X^2+y^2-14y=48

Solution for X^2+y^2-14y=48 equation:

X^2+X^2-14X=48

We move all terms to the left:

X^2+X^2-14X-(48)=0

We add all the numbers together, and all the variables

2X^2-14X-48=0

a = 2; b = -14; c = -48;
Δ = b2-4ac
Δ = -142-4·2·(-48)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{145}}{2*2}=\frac{14-2\sqrt{145}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{145}}{2*2}=\frac{14+2\sqrt{145}}{4}
$