1/10x+480=1/2x

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Solution for 1/10x+480=1/2x equation:



1/10x+480=1/2x
We move all terms to the left:
1/10x+480-(1/2x)=0
Domain of the equation: 10x!=0
x!=0/10
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
1/10x-(+1/2x)+480=0
We get rid of parentheses
1/10x-1/2x+480=0
We calculate fractions
2x/20x^2+(-10x)/20x^2+480=0
We multiply all the terms by the denominator
2x+(-10x)+480*20x^2=0
Wy multiply elements
9600x^2+2x+(-10x)=0
We get rid of parentheses
9600x^2+2x-10x=0
We add all the numbers together, and all the variables
9600x^2-8x=0
a = 9600; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·9600·0
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*9600}=\frac{0}{19200} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*9600}=\frac{16}{19200} =1/1200 $

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