(x*(x-1))/2=15

Solution for (x*(x-1))/2=15 equation:

(x*(x-1))/2=15

We move all terms to the left:

(x*(x-1))/2-(15)=0

We multiply all the terms by the denominator


(x*(x-1))-15*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)-30=0

We get rid of parentheses

x^2-1x-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$