24n^2+55n=24

Solution for 24n^2+55n=24 equation:

24n^2+55n=24

We move all terms to the left:

24n^2+55n-(24)=0

a = 24; b = 55; c = -24;
Δ = b2-4ac
Δ = 552-4·24·(-24)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-73}{2*24}=\frac{-128}{48}
=-2+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+73}{2*24}=\frac{18}{48}
=3/8
$