1/2x-5=1/3x-6

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Solution for 1/2x-5=1/3x-6 equation:



1/2x-5=1/3x-6
We move all terms to the left:
1/2x-5-(1/3x-6)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x-6)!=0
x∈R
We get rid of parentheses
1/2x-1/3x+6-5=0
We calculate fractions
3x/6x^2+(-2x)/6x^2+6-5=0
We add all the numbers together, and all the variables
3x/6x^2+(-2x)/6x^2+1=0
We multiply all the terms by the denominator
3x+(-2x)+1*6x^2=0
Wy multiply elements
6x^2+3x+(-2x)=0
We get rid of parentheses
6x^2+3x-2x=0
We add all the numbers together, and all the variables
6x^2+x=0
a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
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*6}=\frac{-2}{12} =-1/6 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*6}=\frac{0}{12} =0 $

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