n^2-14n-92=0

Solution for n^2-14n-92=0 equation:

n^2-14n-92=0

a = 1; b = -14; c = -92;
Δ = b2-4ac
Δ = -142-4·1·(-92)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{141}}{2*1}=\frac{14-2\sqrt{141}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{141}}{2*1}=\frac{14+2\sqrt{141}}{2}
$