y^2-20y+100=y-10

Solution for y^2-20y+100=y-10 equation:

y^2-20y+100=y-10

We move all terms to the left:

y^2-20y+100-(y-10)=0

We get rid of parentheses

y^2-20y-y+10+100=0

We add all the numbers together, and all the variables

y^2-21y+110=0

a = 1; b = -21; c = +110;
Δ = b2-4ac
Δ = -212-4·1·110
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-1}{2*1}=\frac{20}{2}
=10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+1}{2*1}=\frac{22}{2}
=11
$