-8n^2-10n+137=0

Solution for -8n^2-10n+137=0 equation:

-8n^2-10n+137=0

a = -8; b = -10; c = +137;
Δ = b2-4ac
Δ = -102-4·(-8)·137
Δ = 4484
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:

$\sqrt{\Delta}=\sqrt{4484}=\sqrt{4*1121}=\sqrt{4}*\sqrt{1121}=2\sqrt{1121}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{1121}}{2*-8}=\frac{10-2\sqrt{1121}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{1121}}{2*-8}=\frac{10+2\sqrt{1121}}{-16}
$