x(0.15+x)/(0.10-x)=1.0*10-5

Solution for x(0.15+x)/(0.10-x)=1.0*10-5 equation:

x(0.15+x)/(0.10-x)=1.0*10-5

We move all terms to the left:

x(0.15+x)/(0.10-x)-(1.0*10-5)=0


Domain of the equation: (0.10-x)!=0

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

-x!=-0.10

x!=-0.10/-1

x!=0.10/1

x∈R


We add all the numbers together, and all the variables

x(x+0.15)/(-1x+0.1)-5=0

We multiply all the terms by the denominator


x(x+0.15)-5*(-1x+0.1)=0

We multiply parentheses

x^2+0.15x+5x-0.5=0

We add all the numbers together, and all the variables

x^2+5.15x-0.5=0

a = 1; b = 5.15; c = -0.5;
Δ = b2-4ac
Δ = 5.152-4·1·(-0.5)
Δ = 28.5225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5.15)-\sqrt{28.5225}}{2*1}=\frac{-5.15-\sqrt{28.5225}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.15)+\sqrt{28.5225}}{2*1}=\frac{-5.15+\sqrt{28.5225}}{2}
$