8n^2-16n-92=0

Solution for 8n^2-16n-92=0 equation:

8n^2-16n-92=0

a = 8; b = -16; c = -92;
Δ = b2-4ac
Δ = -162-4·8·(-92)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-40\sqrt{2}}{2*8}=\frac{16-40\sqrt{2}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+40\sqrt{2}}{2*8}=\frac{16+40\sqrt{2}}{16}
$