x=1100+10/100x

Solution for x=1100+10/100x equation:

x=1100+10/100x

We move all terms to the left:

x-(1100+10/100x)=0


Domain of the equation: 100x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(10/100x+1100)=0

We get rid of parentheses

x-10/100x-1100=0

We multiply all the terms by the denominator


x*100x-1100*100x-10=0

Wy multiply elements

100x^2-110000x-10=0

a = 100; b = -110000; c = -10;
Δ = b2-4ac
Δ = -1100002-4·100·(-10)
Δ = 12100004000
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:

$\sqrt{\Delta}=\sqrt{12100004000}=\sqrt{400*30250010}=\sqrt{400}*\sqrt{30250010}=20\sqrt{30250010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110000)-20\sqrt{30250010}}{2*100}=\frac{110000-20\sqrt{30250010}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110000)+20\sqrt{30250010}}{2*100}=\frac{110000+20\sqrt{30250010}}{200}
$