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

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
$