y*(y+2)/2=180

Solution for y*(y+2)/2=180 equation:

y(y+2)/2=180

We move all terms to the left:

y(y+2)/2-(180)=0

We multiply all the terms by the denominator


y(y+2)-180*2=0

We add all the numbers together, and all the variables

y(y+2)-360=0

We multiply parentheses

y^2+2y-360=0

a = 1; b = 2; c = -360;
Δ = b2-4ac
Δ = 22-4·1·(-360)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*1}=\frac{-40}{2}
=-20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*1}=\frac{36}{2}
=18
$