1/2x+3=1/10x

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Solution for 1/2x+3=1/10x equation:



1/2x+3=1/10x
We move all terms to the left:
1/2x+3-(1/10x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 10x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x-(+1/10x)+3=0
We get rid of parentheses
1/2x-1/10x+3=0
We calculate fractions
10x/20x^2+(-2x)/20x^2+3=0
We multiply all the terms by the denominator
10x+(-2x)+3*20x^2=0
Wy multiply elements
60x^2+10x+(-2x)=0
We get rid of parentheses
60x^2+10x-2x=0
We add all the numbers together, and all the variables
60x^2+8x=0
a = 60; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·60·0
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*60}=\frac{-16}{120} =-2/15 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*60}=\frac{0}{120} =0 $

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