x+18/100*x=118

Solution for x+18/100*x=118 equation:

x+18/100x=118

We move all terms to the left:

x+18/100x-(118)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-118*100x+18=0

Wy multiply elements

100x^2-11800x+18=0

a = 100; b = -11800; c = +18;
Δ = b2-4ac
Δ = -118002-4·100·18
Δ = 139232800
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:

$\sqrt{\Delta}=\sqrt{139232800}=\sqrt{211600*658}=\sqrt{211600}*\sqrt{658}=460\sqrt{658}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11800)-460\sqrt{658}}{2*100}=\frac{11800-460\sqrt{658}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11800)+460\sqrt{658}}{2*100}=\frac{11800+460\sqrt{658}}{200}
$