X(x-1)/2=210

Solution for X(x-1)/2=210 equation:

X(X-1)/2=210

We move all terms to the left:

X(X-1)/2-(210)=0

We multiply all the terms by the denominator


X(X-1)-210*2=0

We add all the numbers together, and all the variables

X(X-1)-420=0

We multiply parentheses

X^2-1X-420=0

a = 1; b = -1; c = -420;
Δ = b2-4ac
Δ = -12-4·1·(-420)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-41}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+41}{2*1}=\frac{42}{2}
=21
$