2/3x-4-1/20=5/6x-8

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Solution for 2/3x-4-1/20=5/6x-8 equation:



2/3x-4-1/20=5/6x-8
We move all terms to the left:
2/3x-4-1/20-(5/6x-8)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x-8)!=0
x∈R
We get rid of parentheses
2/3x-5/6x+8-4-1/20=0
We calculate fractions
(-108x^2)/720x^2+480x/720x^2+(-600x)/720x^2+8-4=0
We add all the numbers together, and all the variables
(-108x^2)/720x^2+480x/720x^2+(-600x)/720x^2+4=0
We multiply all the terms by the denominator
(-108x^2)+480x+(-600x)+4*720x^2=0
Wy multiply elements
(-108x^2)+2880x^2+480x+(-600x)=0
We get rid of parentheses
-108x^2+2880x^2+480x-600x=0
We add all the numbers together, and all the variables
2772x^2-120x=0
a = 2772; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·2772·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*2772}=\frac{0}{5544} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*2772}=\frac{240}{5544} =10/231 $

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