(4x)/(1+x)=3x

Solution for (4x)/(1+x)=3x equation:

(4x)/(1+x)=3x

We move all terms to the left:

(4x)/(1+x)-(3x)=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∈R


We add all the numbers together, and all the variables

4x/(x+1)-3x=0

We add all the numbers together, and all the variables

-3x+4x/(x+1)=0

We multiply all the terms by the denominator


-3x*(x+1)+4x=0

We add all the numbers together, and all the variables

4x-3x*(x+1)=0

We multiply parentheses

-3x^2+4x-3x=0

We add all the numbers together, and all the variables

-3x^2+x=0

a = -3; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-3)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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