(39-x)*100/x=x

Solution for (39-x)*100/x=x equation:

(39-x)*100/x=x

We move all terms to the left:

(39-x)*100/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(-1x+39)*100/x-x=0

We add all the numbers together, and all the variables

-1x+(-1x+39)*100/x=0

We multiply all the terms by the denominator


-1x*x+(-1x+39)*100=0

We multiply parentheses

-1x*x-100x+3900=0

Wy multiply elements

-1x^2-100x+3900=0

a = -1; b = -100; c = +3900;
Δ = b2-4ac
Δ = -1002-4·(-1)·3900
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-160}{2*-1}=\frac{-60}{-2}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+160}{2*-1}=\frac{260}{-2}
=-130
$