8n^2+40n+47=0

Solution for 8n^2+40n+47=0 equation:

8n^2+40n+47=0

a = 8; b = 40; c = +47;
Δ = b2-4ac
Δ = 402-4·8·47
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{6}}{2*8}=\frac{-40-4\sqrt{6}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{6}}{2*8}=\frac{-40+4\sqrt{6}}{16}
$