100/x+25=50-X

Solution for 100/x+25=50-X equation:

100/x+25=50-x

We move all terms to the left:

100/x+25-(50-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

100/x-(-1x+50)+25=0

We get rid of parentheses

100/x+1x-50+25=0

We multiply all the terms by the denominator


1x*x-50*x+25*x+100=0

We add all the numbers together, and all the variables

-25x+1x*x+100=0

Wy multiply elements

x^2-25x+100=0

a = 1; b = -25; c = +100;
Δ = b2-4ac
Δ = -252-4·1·100
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-15}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+15}{2*1}=\frac{40}{2}
=20
$