1/6x+2=2/5x+1

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



1/6x+2=2/5x+1
We move all terms to the left:
1/6x+2-(2/5x+1)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 5x+1)!=0
x∈R
We get rid of parentheses
1/6x-2/5x-1+2=0
We calculate fractions
5x/30x^2+(-12x)/30x^2-1+2=0
We add all the numbers together, and all the variables
5x/30x^2+(-12x)/30x^2+1=0
We multiply all the terms by the denominator
5x+(-12x)+1*30x^2=0
Wy multiply elements
30x^2+5x+(-12x)=0
We get rid of parentheses
30x^2+5x-12x=0
We add all the numbers together, and all the variables
30x^2-7x=0
a = 30; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·30·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*30}=\frac{0}{60} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*30}=\frac{14}{60} =7/30 $

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