x(x-2)/2=105

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

x(x-2)/2=105

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x(x-2)-210=0

We multiply parentheses

x^2-2x-210=0

a = 1; b = -2; c = -210;
Δ = b2-4ac
Δ = -22-4·1·(-210)
Δ = 844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{211}}{2*1}=\frac{2-2\sqrt{211}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{211}}{2*1}=\frac{2+2\sqrt{211}}{2}
$