(10x+10)*x/(10x+10)+x=x+10

Solution for (10x+10)*x/(10x+10)+x=x+10 equation:

(10x+10)*x/(10x+10)+x=x+10

We move all terms to the left:

(10x+10)*x/(10x+10)+x-(x+10)=0


Domain of the equation: (10x+10)!=0

We move all terms containing x to the left, all other terms to the right

10x!=-10

x!=-10/10

x!=-1

x∈R


We add all the numbers together, and all the variables

x+(10x+10)*x/(10x+10)-(x+10)=0

We get rid of parentheses

x+(10x+10)*x/(10x+10)-x-10=0

We multiply all the terms by the denominator


x*(10x+10)+(10x+10)*x-x*(10x+10)-10*(10x+10)=0

We multiply parentheses

10x^2+10x^2-10x^2+10x+10x-10x-100x-100=0

We add all the numbers together, and all the variables

10x^2-90x-100=0

a = 10; b = -90; c = -100;
Δ = b2-4ac
Δ = -902-4·10·(-100)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-110}{2*10}=\frac{-20}{20}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+110}{2*10}=\frac{200}{20}
=10
$