X2+y2-10y+9=0

Solution for X2+y2-10y+9=0 equation:

X2+X2-10X+9=0

We add all the numbers together, and all the variables

2X^2-10X+9=0

a = 2; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·2·9
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*2}=\frac{10-2\sqrt{7}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*2}=\frac{10+2\sqrt{7}}{4}
$