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

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

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

We move all terms to the left:

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

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

We add all the numbers together, and all the variables

-2x^2+5x+1=0

a = -2; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-2)·1
Δ = 33
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)-\sqrt{33}}{2*-2}=\frac{-5-\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*-2}=\frac{-5+\sqrt{33}}{-4}
$