y^2+21y=100

Solution for y^2+21y=100 equation:

y^2+21y=100

We move all terms to the left:

y^2+21y-(100)=0

a = 1; b = 21; c = -100;
Δ = b2-4ac
Δ = 212-4·1·(-100)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-29}{2*1}=\frac{-50}{2}
=-25
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+29}{2*1}=\frac{8}{2}
=4
$