4/3x+3/2=1/2x+6

Solution for 4/3x+3/2=1/2x+6 equation:

4/3x+3/2=1/2x+6

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


32x/24x^2+(-3x)/24x^2+9x/24x^2-6=0

We multiply all the terms by the denominator


32x+(-3x)+9x-6*24x^2=0

We add all the numbers together, and all the variables

41x+(-3x)-6*24x^2=0

Wy multiply elements

-144x^2+41x+(-3x)=0

We get rid of parentheses

-144x^2+41x-3x=0

We add all the numbers together, and all the variables

-144x^2+38x=0

a = -144; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-144)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-144}=\frac{-76}{-288}
=19/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-144}=\frac{0}{-288}
=0
$