100=25+y^2+2y+1

Solution for 100=25+y^2+2y+1 equation:

100=25+y^2+2y+1

We move all terms to the left:

100-(25+y^2+2y+1)=0

We get rid of parentheses

-y^2-2y-25-1+100=0

We add all the numbers together, and all the variables

-1y^2-2y+74=0

a = -1; b = -2; c = +74;
Δ = b2-4ac
Δ = -22-4·(-1)·74
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10\sqrt{3}}{2*-1}=\frac{2-10\sqrt{3}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10\sqrt{3}}{2*-1}=\frac{2+10\sqrt{3}}{-2}
$