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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(-8a(a+4)-(2a+1)), so:

-8a(a+4)-(2a+1)

We multiply parentheses

-8a^2-32a-(2a+1)

We get rid of parentheses

-8a^2-32a-2a-1

We add all the numbers together, and all the variables

-8a^2-34a-1

Back to the equation:

-(-8a^2-34a-1)


We get rid of parentheses

8a^2+34a+1-19=0

We add all the numbers together, and all the variables

8a^2+34a-18=0

a = 8; b = 34; c = -18;
Δ = b2-4ac
Δ = 342-4·8·(-18)
Δ = 1732
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:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{433}}{2*8}=\frac{-34-2\sqrt{433}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{433}}{2*8}=\frac{-34+2\sqrt{433}}{16}
$