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)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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