4n^2=20n+24

Solution for 4n^2=20n+24 equation:

4n^2=20n+24

We move all terms to the left:

4n^2-(20n+24)=0

We get rid of parentheses

4n^2-20n-24=0

a = 4; b = -20; c = -24;
Δ = b2-4ac
Δ = -202-4·4·(-24)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-28}{2*4}=\frac{-8}{8}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+28}{2*4}=\frac{48}{8}
=6
$