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 = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{85}}{2*-10}=\frac{-40-4\sqrt{85}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{85}}{2*-10}=\frac{-40+4\sqrt{85}}{-20}
$