x-5/6+2-x/3x-6/5=-3

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Solution for x-5/6+2-x/3x-6/5=-3 equation:



x-5/6+2-x/3x-6/5=-3
We move all terms to the left:
x-5/6+2-x/3x-6/5-(-3)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
x-x/3x+5-5/6-6/5=0
We calculate fractions
x+(-150x)/450x+(-375x)/450x+(-648x)/450x+5=0
We multiply all the terms by the denominator
x*450x+(-150x)+(-375x)+(-648x)+5*450x=0
Wy multiply elements
450x^2+(-150x)+(-375x)+(-648x)+2250x=0
We get rid of parentheses
450x^2-150x-375x-648x+2250x=0
We add all the numbers together, and all the variables
450x^2+1077x=0
a = 450; b = 1077; c = 0;
Δ = b2-4ac
Δ = 10772-4·450·0
Δ = 1159929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1159929}=1077$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1077)-1077}{2*450}=\frac{-2154}{900} =-2+59/150 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1077)+1077}{2*450}=\frac{0}{900} =0 $

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