8n(4n+5)=19

Solution for 8n(4n+5)=19 equation:

8n(4n+5)=19

We move all terms to the left:

8n(4n+5)-(19)=0

We multiply parentheses

32n^2+40n-19=0

a = 32; b = 40; c = -19;
Δ = b2-4ac
Δ = 402-4·32·(-19)
Δ = 4032
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-24\sqrt{7}}{2*32}=\frac{-40-24\sqrt{7}}{64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+24\sqrt{7}}{2*32}=\frac{-40+24\sqrt{7}}{64}
$