4/3x-1/6=3/2x+8

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Solution for 4/3x-1/6=3/2x+8 equation:



4/3x-1/6=3/2x+8
We move all terms to the left:
4/3x-1/6-(3/2x+8)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x+8)!=0
x∈R
We get rid of parentheses
4/3x-3/2x-8-1/6=0
We calculate fractions
(-12x^2)/216x^2+288x/216x^2+(-324x)/216x^2-8=0
We multiply all the terms by the denominator
(-12x^2)+288x+(-324x)-8*216x^2=0
Wy multiply elements
(-12x^2)-1728x^2+288x+(-324x)=0
We get rid of parentheses
-12x^2-1728x^2+288x-324x=0
We add all the numbers together, and all the variables
-1740x^2-36x=0
a = -1740; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-1740)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-1740}=\frac{0}{-3480} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-1740}=\frac{72}{-3480} =-3/145 $

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