3(x-2)=4(31/2x)

Solution for 3(x-2)=4(31/2x) equation:

3(x-2)=4(31/2x)

We move all terms to the left:

3(x-2)-(4(31/2x))=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(x-2)-(4(+31/2x))=0

We multiply parentheses

3x-(4(+31/2x))-6=0

We multiply all the terms by the denominator


3x*2x))-(4(-6*2x))+31=0

Wy multiply elements

6x^2-12x=0

a = 6; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·6·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*6}=\frac{24}{12}
=2
$