3/2x=6(4-x)/2

Solution for 3/2x=6(4-x)/2 equation:

3/2x=6(4-x)/2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: +(-(6(-1x+4)*2x)+(), so:

-(6(-1x+4)*2x)+(

We add all the numbers together, and all the variables

-(6(-1x+4)*2x)


We calculate terms in parentheses: -(6(-1x+4)*2x), so:

6(-1x+4)*2x

We multiply parentheses

-12x^2+48x

Back to the equation:

-(-12x^2+48x)


We get rid of parentheses

12x^2-48x

Back to the equation:

+(12x^2-48x)


We get rid of parentheses

12x^2-48x=0

a = 12; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·12·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*12}=\frac{96}{24}
=4
$