2/15x+6=3/20x

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Solution for 2/15x+6=3/20x equation:



2/15x+6=3/20x
We move all terms to the left:
2/15x+6-(3/20x)=0
Domain of the equation: 15x!=0
x!=0/15
x!=0
x∈R
Domain of the equation: 20x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2/15x-(+3/20x)+6=0
We get rid of parentheses
2/15x-3/20x+6=0
We calculate fractions
40x/300x^2+(-45x)/300x^2+6=0
We multiply all the terms by the denominator
40x+(-45x)+6*300x^2=0
Wy multiply elements
1800x^2+40x+(-45x)=0
We get rid of parentheses
1800x^2+40x-45x=0
We add all the numbers together, and all the variables
1800x^2-5x=0
a = 1800; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1800·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1800}=\frac{0}{3600} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1800}=\frac{10}{3600} =1/360 $

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