x(x-1)/2=105

Solution for x(x-1)/2=105 equation:

x(x-1)/2=105

We move all terms to the left:

x(x-1)/2-(105)=0

We multiply all the terms by the denominator


x(x-1)-105*2=0

We add all the numbers together, and all the variables

x(x-1)-210=0

We multiply parentheses

x^2-1x-210=0

a = 1; b = -1; c = -210;
Δ = b2-4ac
Δ = -12-4·1·(-210)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-29}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*1}=\frac{30}{2}
=15
$