n2+14n-55=0

Solution for n2+14n-55=0 equation:

n2+14n-55=0

We add all the numbers together, and all the variables

n^2+14n-55=0

a = 1; b = 14; c = -55;
Δ = b2-4ac
Δ = 142-4·1·(-55)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{26}}{2*1}=\frac{-14-4\sqrt{26}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{26}}{2*1}=\frac{-14+4\sqrt{26}}{2}
$