-y+21^2-y^2=126

Solution for -y+21^2-y^2=126 equation:

-y+21^2-y^2=126

We move all terms to the left:

-y+21^2-y^2-(126)=0

determiningTheFunctionDomain
-y^2-y-126+21^2=0

We add all the numbers together, and all the variables

-1y^2-1y+315=0

a = -1; b = -1; c = +315;
Δ = b2-4ac
Δ = -12-4·(-1)·315
Δ = 1261
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1261}}{2*-1}=\frac{1-\sqrt{1261}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1261}}{2*-1}=\frac{1+\sqrt{1261}}{-2}
$