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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-8a^2+32a+6a+3-19=0

We add all the numbers together, and all the variables

-8a^2+38a-16=0

a = -8; b = 38; c = -16;
Δ = b2-4ac
Δ = 382-4·(-8)·(-16)
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{233}}{2*-8}=\frac{-38-2\sqrt{233}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{233}}{2*-8}=\frac{-38+2\sqrt{233}}{-16}
$