2/(1-x)=3x+4

Solution for 2/(1-x)=3x+4 equation:

2/(1-x)=3x+4

We move all terms to the left:

2/(1-x)-(3x+4)=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

2/(-1x+1)-(3x+4)=0

We get rid of parentheses

2/(-1x+1)-3x-4=0

We multiply all the terms by the denominator


-3x*(-1x+1)-4*(-1x+1)+2=0

We multiply parentheses

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

We add all the numbers together, and all the variables

3x^2+x-2=0

a = 3; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·3·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*3}=\frac{4}{6}
=2/3
$