(x*(x-1))/2=90

Solution for (x*(x-1))/2=90 equation:

(x(x-1))/2=90

We move all terms to the left:

(x(x-1))/2-(90)=0

We multiply all the terms by the denominator


(x(x-1))-90*2=0


We calculate terms in parentheses: +(x(x-1)), so:

x(x-1)

We multiply parentheses

x^2-1x

Back to the equation:

+(x^2-1x)


We add all the numbers together, and all the variables

(x^2-1x)-180=0

We get rid of parentheses

x^2-1x-180=0

a = 1; b = -1; c = -180;
Δ = b2-4ac
Δ = -12-4·1·(-180)
Δ = 721
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{721}}{2*1}=\frac{1-\sqrt{721}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{721}}{2*1}=\frac{1+\sqrt{721}}{2}
$