8+6/5a=2a

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Solution for 8+6/5a=2a equation:



8+6/5a=2a
We move all terms to the left:
8+6/5a-(2a)=0
Domain of the equation: 5a!=0
a!=0/5
a!=0
a∈R
We add all the numbers together, and all the variables
-2a+6/5a+8=0
We multiply all the terms by the denominator
-2a*5a+8*5a+6=0
Wy multiply elements
-10a^2+40a+6=0
a = -10; b = 40; c = +6;
Δ = b2-4ac
Δ = 402-4·(-10)·6
Δ = 1840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{115}}{2*-10}=\frac{-40-4\sqrt{115}}{-20} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{115}}{2*-10}=\frac{-40+4\sqrt{115}}{-20} $

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