8+6/5a=2a

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}
$