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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-x*2x+1*2x+4=0

Wy multiply elements

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

a = -2; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-2)·4
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-2}=\frac{4}{-4}
=-1
$