x/(1-x)-4x=0

Solution for x/(1-x)-4x=0 equation:

x/(1-x)-4x=0


Domain of the equation: (1-x)!=0

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

-x!=-1

x!=-1/-1

x!=1

x∈R


We add all the numbers together, and all the variables

x/(-1x+1)-4x=0

We add all the numbers together, and all the variables

-4x+x/(-1x+1)=0

We multiply all the terms by the denominator


-4x*(-1x+1)+x=0

We add all the numbers together, and all the variables

x-4x*(-1x+1)=0

We multiply parentheses

4x^2+x-4x=0

We add all the numbers together, and all the variables

4x^2-3x=0

a = 4; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·4·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*4}=\frac{6}{8}
=3/4
$