1/2x+4=13/18x

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Solution for 1/2x+4=13/18x equation:



1/2x+4=13/18x
We move all terms to the left:
1/2x+4-(13/18x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 18x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x-(+13/18x)+4=0
We get rid of parentheses
1/2x-13/18x+4=0
We calculate fractions
18x/36x^2+(-26x)/36x^2+4=0
We multiply all the terms by the denominator
18x+(-26x)+4*36x^2=0
Wy multiply elements
144x^2+18x+(-26x)=0
We get rid of parentheses
144x^2+18x-26x=0
We add all the numbers together, and all the variables
144x^2-8x=0
a = 144; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·144·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*144}=\frac{0}{288} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*144}=\frac{16}{288} =1/18 $

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