n^2-3n-24=6

Solution for n^2-3n-24=6 equation:

n^2-3n-24=6

We move all terms to the left:

n^2-3n-24-(6)=0

We add all the numbers together, and all the variables

n^2-3n-30=0

a = 1; b = -3; c = -30;
Δ = b2-4ac
Δ = -32-4·1·(-30)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{129}}{2*1}=\frac{3-\sqrt{129}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{129}}{2*1}=\frac{3+\sqrt{129}}{2}
$