X^2+y^2-5y=6

Solution for X^2+y^2-5y=6 equation:

X^2+X^2-5X=6

We move all terms to the left:

X^2+X^2-5X-(6)=0

We add all the numbers together, and all the variables

2X^2-5X-6=0

a = 2; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·2·(-6)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{73}}{2*2}=\frac{5-\sqrt{73}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*2}=\frac{5+\sqrt{73}}{4}
$