0.01x+0.01=1/100x+.1

Solution for 0.01x+0.01=1/100x+.1 equation:

0.01x+0.01=1/100x+.1

We move all terms to the left:

0.01x+0.01-(1/100x+.1)=0


Domain of the equation: 100x+.1)!=0

x∈R


We add all the numbers together, and all the variables

0.01x-(1/100x+0.1)+0.01=0

We get rid of parentheses

0.01x-1/100x-0.1+0.01=0

We multiply all the terms by the denominator


(0.01x)*100x-(0.1)*100x+(0.01)*100x-1=0

We add all the numbers together, and all the variables

(+0.01x)*100x-(0.1)*100x+(0.01)*100x-1=0

We multiply parentheses

0x^2-10x+x-1=0

We add all the numbers together, and all the variables

x^2-9x-1=0

a = 1; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·1·(-1)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{85}}{2*1}=\frac{9-\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{85}}{2*1}=\frac{9+\sqrt{85}}{2}
$