2a(4a+1)=3a

Solution for 2a(4a+1)=3a equation:

2a(4a+1)=3a

We move all terms to the left:

2a(4a+1)-(3a)=0

We add all the numbers together, and all the variables

-3a+2a(4a+1)=0

We multiply parentheses

8a^2-3a+2a=0

We add all the numbers together, and all the variables

8a^2-1a=0

a = 8; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·8·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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