n^2-14n-7=0

Solution for n^2-14n-7=0 equation:

n^2-14n-7=0

a = 1; b = -14; c = -7;
Δ = b2-4ac
Δ = -142-4·1·(-7)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{14}}{2*1}=\frac{14-4\sqrt{14}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{14}}{2*1}=\frac{14+4\sqrt{14}}{2}
$