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

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

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

We move all terms to the left:

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


Domain of the equation: (x+1)!=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)-(-1x+3)=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

We add all the numbers together, and all the variables

x^2+2x-3=0

a = 1; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*1}=\frac{2}{2}
=1
$