50/(20-2x)=10-x

Solution for 50/(20-2x)=10-x equation:

50/(20-2x)=10-x

We move all terms to the left:

50/(20-2x)-(10-x)=0


Domain of the equation: (20-2x)!=0

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

-2x!=-20

x!=-20/-2

x!=+10

x∈R


We add all the numbers together, and all the variables

50/(-2x+20)-(-1x+10)=0

We get rid of parentheses

50/(-2x+20)+1x-10=0

We multiply all the terms by the denominator


1x*(-2x+20)-10*(-2x+20)+50=0

We multiply parentheses

-2x^2+20x+20x-200+50=0

We add all the numbers together, and all the variables

-2x^2+40x-150=0

a = -2; b = 40; c = -150;
Δ = b2-4ac
Δ = 402-4·(-2)·(-150)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20}{2*-2}=\frac{-60}{-4}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20}{2*-2}=\frac{-20}{-4}
=+5
$