n2-4n-27=0

Solution for n2-4n-27=0 equation:

n2-4n-27=0

We add all the numbers together, and all the variables

n^2-4n-27=0

a = 1; b = -4; c = -27;
Δ = b2-4ac
Δ = -42-4·1·(-27)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{31}}{2*1}=\frac{4-2\sqrt{31}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{31}}{2*1}=\frac{4+2\sqrt{31}}{2}
$