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

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

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

We move all terms to the left:

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


Domain of the equation: (2x+2)!=0

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

2x!=-2

x!=-2/2

x!=-1

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(2x^2+2x)/(4x^2+4x)+(-6x-6)/(4x^2+4x)=0

We multiply all the terms by the denominator


(2x^2+2x)+(-6x-6)=0

We get rid of parentheses

2x^2+2x-6x-6=0

We add all the numbers together, and all the variables

2x^2-4x-6=0

a = 2; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·2·(-6)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*2}=\frac{12}{4}
=3
$