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

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



1/3x+3=2/5x-1
We move all terms to the left:
1/3x+3-(2/5x-1)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x-1)!=0
x∈R
We get rid of parentheses
1/3x-2/5x+1+3=0
We calculate fractions
5x/15x^2+(-6x)/15x^2+1+3=0
We add all the numbers together, and all the variables
5x/15x^2+(-6x)/15x^2+4=0
We multiply all the terms by the denominator
5x+(-6x)+4*15x^2=0
Wy multiply elements
60x^2+5x+(-6x)=0
We get rid of parentheses
60x^2+5x-6x=0
We add all the numbers together, and all the variables
60x^2-1x=0
a = 60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·60·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*60}=\frac{0}{120} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*60}=\frac{2}{120} =1/60 $

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