-24-5n+n^2=1

Solution for -24-5n+n^2=1 equation:

-24-5n+n^2=1

We move all terms to the left:

-24-5n+n^2-(1)=0

We add all the numbers together, and all the variables

n^2-5n-25=0

a = 1; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·1·(-25)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{5}}{2*1}=\frac{5-5\sqrt{5}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{5}}{2*1}=\frac{5+5\sqrt{5}}{2}
$