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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x-2x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2+8x-2=0

a = 4; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·4·(-2)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*4}=\frac{-8-4\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*4}=\frac{-8+4\sqrt{6}}{8}
$