y+y(y+500)=1210

Solution for y+y(y+500)=1210 equation:

y+y(y+500)=1210

We move all terms to the left:

y+y(y+500)-(1210)=0

We multiply parentheses

y^2+y+500y-1210=0

We add all the numbers together, and all the variables

y^2+501y-1210=0

a = 1; b = 501; c = -1210;
Δ = b2-4ac
Δ = 5012-4·1·(-1210)
Δ = 255841
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{-(501)-\sqrt{255841}}{2*1}=\frac{-501-\sqrt{255841}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(501)+\sqrt{255841}}{2*1}=\frac{-501+\sqrt{255841}}{2}
$