x(x-100)=120000

Solution for x(x-100)=120000 equation:

x(x-100)=120000

We move all terms to the left:

x(x-100)-(120000)=0

We multiply parentheses

x^2-100x-120000=0

a = 1; b = -100; c = -120000;
Δ = b2-4ac
Δ = -1002-4·1·(-120000)
Δ = 490000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{490000}=700$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-700}{2*1}=\frac{-600}{2}
=-300
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+700}{2*1}=\frac{800}{2}
=400
$