-8a(-4a)+3(2a+1)=19

Solution for -8a(-4a)+3(2a+1)=19 equation:

-8a(-4a)+3(2a+1)=19

We move all terms to the left:

-8a(-4a)+3(2a+1)-(19)=0

We multiply parentheses

32a^2+6a+3-19=0

We add all the numbers together, and all the variables

32a^2+6a-16=0

a = 32; b = 6; c = -16;
Δ = b2-4ac
Δ = 62-4·32·(-16)
Δ = 2084
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:

$\sqrt{\Delta}=\sqrt{2084}=\sqrt{4*521}=\sqrt{4}*\sqrt{521}=2\sqrt{521}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{521}}{2*32}=\frac{-6-2\sqrt{521}}{64}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{521}}{2*32}=\frac{-6+2\sqrt{521}}{64}
$