n2-12n-45=0

Solution for n2-12n-45=0 equation:

n2-12n-45=0

We add all the numbers together, and all the variables

n^2-12n-45=0

a = 1; b = -12; c = -45;
Δ = b2-4ac
Δ = -122-4·1·(-45)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*1}=\frac{-6}{2}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*1}=\frac{30}{2}
=15
$