x-20/100x=120

Solution for x-20/100x=120 equation:

x-20/100x=120

We move all terms to the left:

x-20/100x-(120)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-120*100x-20=0

Wy multiply elements

100x^2-12000x-20=0

a = 100; b = -12000; c = -20;
Δ = b2-4ac
Δ = -120002-4·100·(-20)
Δ = 144008000
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:

$\sqrt{\Delta}=\sqrt{144008000}=\sqrt{1600*90005}=\sqrt{1600}*\sqrt{90005}=40\sqrt{90005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12000)-40\sqrt{90005}}{2*100}=\frac{12000-40\sqrt{90005}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12000)+40\sqrt{90005}}{2*100}=\frac{12000+40\sqrt{90005}}{200}
$