y(y+2)=575

Solution for y(y+2)=575 equation:

y(y+2)=575

We move all terms to the left:

y(y+2)-(575)=0

We multiply parentheses

y^2+2y-575=0

a = 1; b = 2; c = -575;
Δ = b2-4ac
Δ = 22-4·1·(-575)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-48}{2*1}=\frac{-50}{2}
=-25
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+48}{2*1}=\frac{46}{2}
=23
$