x(x+1)/2=180

Solution for x(x+1)/2=180 equation:

x(x+1)/2=180

We move all terms to the left:

x(x+1)/2-(180)=0

We multiply all the terms by the denominator


x(x+1)-180*2=0

We add all the numbers together, and all the variables

x(x+1)-360=0

We multiply parentheses

x^2+x-360=0

a = 1; b = 1; c = -360;
Δ = b2-4ac
Δ = 12-4·1·(-360)
Δ = 1441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1441}}{2*1}=\frac{-1-\sqrt{1441}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1441}}{2*1}=\frac{-1+\sqrt{1441}}{2}
$