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

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

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

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

6x-(4(3/2x+1))+4=0

We multiply all the terms by the denominator


6x*2x+4*2x+1))-(4(3+1))=0

We add all the numbers together, and all the variables

6x*2x+4*2x+1))-(44)=0

We add all the numbers together, and all the variables

6x*2x+4*2x=0

Wy multiply elements

12x^2+8x=0

a = 12; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·12·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*12}=\frac{-16}{24}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*12}=\frac{0}{24}
=0
$