3/2x+4=1/6x-5

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Solution for 3/2x+4=1/6x-5 equation:



3/2x+4=1/6x-5
We move all terms to the left:
3/2x+4-(1/6x-5)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 6x-5)!=0
x∈R
We get rid of parentheses
3/2x-1/6x+5+4=0
We calculate fractions
18x/12x^2+(-2x)/12x^2+5+4=0
We add all the numbers together, and all the variables
18x/12x^2+(-2x)/12x^2+9=0
We multiply all the terms by the denominator
18x+(-2x)+9*12x^2=0
Wy multiply elements
108x^2+18x+(-2x)=0
We get rid of parentheses
108x^2+18x-2x=0
We add all the numbers together, and all the variables
108x^2+16x=0
a = 108; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·108·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*108}=\frac{-32}{216} =-4/27 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*108}=\frac{0}{216} =0 $

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