n^2-10n-112=0

Solution for n^2-10n-112=0 equation:

n^2-10n-112=0

a = 1; b = -10; c = -112;
Δ = b2-4ac
Δ = -102-4·1·(-112)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{137}}{2*1}=\frac{10-2\sqrt{137}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{137}}{2*1}=\frac{10+2\sqrt{137}}{2}
$