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

Solution for (3x+1)/(2x+2)+1-x-1=0 equation:

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


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

We get rid of parentheses

-2x^2-2x+3x+1=0

We add all the numbers together, and all the variables

-2x^2+x+1=0

a = -2; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-2)·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-2}=\frac{2}{-4}
=-1/2
$