8n^2-16n-66=0

Solution for 8n^2-16n-66=0 equation:

8n^2-16n-66=0

a = 8; b = -16; c = -66;
Δ = b2-4ac
Δ = -162-4·8·(-66)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{37}}{2*8}=\frac{16-8\sqrt{37}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{37}}{2*8}=\frac{16+8\sqrt{37}}{16}
$