x+18/100*x=1222

Solution for x+18/100*x=1222 equation:

x+18/100x=1222

We move all terms to the left:

x+18/100x-(1222)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-1222*100x+18=0

Wy multiply elements

100x^2-122200x+18=0

a = 100; b = -122200; c = +18;
Δ = b2-4ac
Δ = -1222002-4·100·18
Δ = 14932832800
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:

$\sqrt{\Delta}=\sqrt{14932832800}=\sqrt{400*37332082}=\sqrt{400}*\sqrt{37332082}=20\sqrt{37332082}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122200)-20\sqrt{37332082}}{2*100}=\frac{122200-20\sqrt{37332082}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122200)+20\sqrt{37332082}}{2*100}=\frac{122200+20\sqrt{37332082}}{200}
$