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

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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
Wy multiply elements
-144x^2+32x+(-3x)+(-9x)=0
We get rid of parentheses
-144x^2+32x-3x-9x=0
We add all the numbers together, and all the variables
-144x^2+20x=0
a = -144; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-144)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-144}=\frac{-40}{-288} =5/36 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-144}=\frac{0}{-288} =0 $

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