n^2-24n+5=-4

Solution for n^2-24n+5=-4 equation:

n^2-24n+5=-4

We move all terms to the left:

n^2-24n+5-(-4)=0

We add all the numbers together, and all the variables

n^2-24n+9=0

a = 1; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·1·9
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{15}}{2*1}=\frac{24-6\sqrt{15}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{15}}{2*1}=\frac{24+6\sqrt{15}}{2}
$