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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


3x*2x-4*2x+1-3=0

We add all the numbers together, and all the variables

3x*2x-4*2x-2=0

Wy multiply elements

6x^2-8x-2=0

a = 6; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·6·(-2)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*6}=\frac{8-4\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*6}=\frac{8+4\sqrt{7}}{12}
$