1/2x+1/5x+1/2=19/10

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Solution for 1/2x+1/5x+1/2=19/10 equation:



1/2x+1/5x+1/2=19/10
We move all terms to the left:
1/2x+1/5x+1/2-(19/10)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x+1/5x+1/2-(+19/10)=0
We get rid of parentheses
1/2x+1/5x+1/2-19/10=0
We calculate fractions
(-1900x^2)/400x^2+50x/400x^2+80x/400x^2+50x/400x^2=0
We multiply all the terms by the denominator
(-1900x^2)+50x+80x+50x=0
We add all the numbers together, and all the variables
(-1900x^2)+180x=0
We get rid of parentheses
-1900x^2+180x=0
a = -1900; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-1900)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-1900}=\frac{-360}{-3800} =9/95 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-1900}=\frac{0}{-3800} =0 $

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