x(x-1)/2=378

Solution for x(x-1)/2=378 equation:

x(x-1)/2=378

We move all terms to the left:

x(x-1)/2-(378)=0

We multiply all the terms by the denominator


x(x-1)-378*2=0

We add all the numbers together, and all the variables

x(x-1)-756=0

We multiply parentheses

x^2-1x-756=0

a = 1; b = -1; c = -756;
Δ = b2-4ac
Δ = -12-4·1·(-756)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-55}{2*1}=\frac{-54}{2}
=-27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+55}{2*1}=\frac{56}{2}
=28
$