3+1/7x=1+1/2x

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Solution for 3+1/7x=1+1/2x equation:



3+1/7x=1+1/2x
We move all terms to the left:
3+1/7x-(1+1/2x)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/7x-(1/2x+1)+3=0
We get rid of parentheses
1/7x-1/2x-1+3=0
We calculate fractions
2x/14x^2+(-7x)/14x^2-1+3=0
We add all the numbers together, and all the variables
2x/14x^2+(-7x)/14x^2+2=0
We multiply all the terms by the denominator
2x+(-7x)+2*14x^2=0
Wy multiply elements
28x^2+2x+(-7x)=0
We get rid of parentheses
28x^2+2x-7x=0
We add all the numbers together, and all the variables
28x^2-5x=0
a = 28; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·28·0
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*28}=\frac{0}{56} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*28}=\frac{10}{56} =5/28 $

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