y(2y+1)=5000

Solution for y(2y+1)=5000 equation:

y(2y+1)=5000

We move all terms to the left:

y(2y+1)-(5000)=0

We multiply parentheses

2y^2+y-5000=0

a = 2; b = 1; c = -5000;
Δ = b2-4ac
Δ = 12-4·2·(-5000)
Δ = 40001
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{40001}}{2*2}=\frac{-1-\sqrt{40001}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{40001}}{2*2}=\frac{-1+\sqrt{40001}}{4}
$