4n^2=4n+24

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

4n^2=4n+24

We move all terms to the left:

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

We get rid of parentheses

4n^2-4n-24=0

a = 4; b = -4; c = -24;
Δ = b2-4ac
Δ = -42-4·4·(-24)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*4}=\frac{-16}{8}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*4}=\frac{24}{8}
=3
$