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

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
$