6/5a=2a

Solution for 6/5a=2a equation:

6/5a=2a

We move all terms to the left:

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=0

We multiply all the terms by the denominator


-2a*5a+6=0

Wy multiply elements

-10a^2+6=0

a = -10; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-10)·6
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-10}=\frac{0-4\sqrt{15}}{-20}
=-\frac{4\sqrt{15}}{-20}
=-\frac{\sqrt{15}}{-5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-10}=\frac{0+4\sqrt{15}}{-20}
=\frac{4\sqrt{15}}{-20}
=\frac{\sqrt{15}}{-5}
$