5n+6=n^2-2n-24

Solution for 5n+6=n^2-2n-24 equation:

5n+6=n^2-2n-24

We move all terms to the left:

5n+6-(n^2-2n-24)=0

We get rid of parentheses

-n^2+5n+2n+24+6=0

We add all the numbers together, and all the variables

-1n^2+7n+30=0

a = -1; b = 7; c = +30;
Δ = b2-4ac
Δ = 72-4·(-1)·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-1}=\frac{-20}{-2}
=+10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-1}=\frac{6}{-2}
=-3
$