1/2x+1/10x-3=3

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



1/2x+1/10x-3=3
We move all terms to the left:
1/2x+1/10x-3-(3)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x+1/10x-6=0
We calculate fractions
10x/20x^2+2x/20x^2-6=0
We multiply all the terms by the denominator
10x+2x-6*20x^2=0
We add all the numbers together, and all the variables
12x-6*20x^2=0
Wy multiply elements
-120x^2+12x=0
a = -120; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-120)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-120}=\frac{-24}{-240} =1/10 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-120}=\frac{0}{-240} =0 $

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