x+10/100x=99

Solution for x+10/100x=99 equation:

x+10/100x=99

We move all terms to the left:

x+10/100x-(99)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-99*100x+10=0

Wy multiply elements

100x^2-9900x+10=0

a = 100; b = -9900; c = +10;
Δ = b2-4ac
Δ = -99002-4·100·10
Δ = 98006000
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:

$\sqrt{\Delta}=\sqrt{98006000}=\sqrt{400*245015}=\sqrt{400}*\sqrt{245015}=20\sqrt{245015}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9900)-20\sqrt{245015}}{2*100}=\frac{9900-20\sqrt{245015}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9900)+20\sqrt{245015}}{2*100}=\frac{9900+20\sqrt{245015}}{200}
$