90=(x+1)(90-x/x)

Solution for 90=(x+1)(90-x/x) equation:

90=(x+1)(90-x/x)

We move all terms to the left:

90-((x+1)(90-x/x))=0


Domain of the equation: x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-((x+1)(-x/x+90))+90=0

We multiply parentheses ..

-((-1x^2+90x-1x+90))+90=0


We calculate terms in parentheses: -((-1x^2+90x-1x+90)), so:

(-1x^2+90x-1x+90)

We get rid of parentheses

-1x^2+90x-1x+90

We add all the numbers together, and all the variables

-1x^2+89x+90

Back to the equation:

-(-1x^2+89x+90)


We get rid of parentheses

1x^2-89x-90+90=0

We add all the numbers together, and all the variables

x^2-89x=0

a = 1; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·1·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*1}=\frac{178}{2}
=89
$