20/4a-1=4/2a

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Solution for 20/4a-1=4/2a equation:



20/4a-1=4/2a
We move all terms to the left:
20/4a-1-(4/2a)=0
Domain of the equation: 4a!=0
a!=0/4
a!=0
a∈R
Domain of the equation: 2a)!=0
a!=0/1
a!=0
a∈R
We add all the numbers together, and all the variables
20/4a-(+4/2a)-1=0
We get rid of parentheses
20/4a-4/2a-1=0
We calculate fractions
40a/8a^2+(-16a)/8a^2-1=0
We multiply all the terms by the denominator
40a+(-16a)-1*8a^2=0
Wy multiply elements
-8a^2+40a+(-16a)=0
We get rid of parentheses
-8a^2+40a-16a=0
We add all the numbers together, and all the variables
-8a^2+24a=0
a = -8; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-8)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-8}=\frac{-48}{-16} =+3 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-8}=\frac{0}{-16} =0 $

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