(20x)/(20+x)+x=75

Solution for (20x)/(20+x)+x=75 equation:

(20x)/(20+x)+x=75

We move all terms to the left:

(20x)/(20+x)+x-(75)=0


Domain of the equation: (20+x)!=0

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

x!=-20

x∈R


We add all the numbers together, and all the variables

20x/(x+20)+x-75=0

We add all the numbers together, and all the variables

x+20x/(x+20)-75=0

We multiply all the terms by the denominator


x*(x+20)+20x-75*(x+20)=0

We add all the numbers together, and all the variables

20x+x*(x+20)-75*(x+20)=0

We multiply parentheses

x^2+20x+20x-75x-1500=0

We add all the numbers together, and all the variables

x^2-35x-1500=0

a = 1; b = -35; c = -1500;
Δ = b2-4ac
Δ = -352-4·1·(-1500)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-85}{2*1}=\frac{-50}{2}
=-25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+85}{2*1}=\frac{120}{2}
=60
$