24n2-56n-160=0

Solution for 24n2-56n-160=0 equation:

24n^2-56n-160=0

a = 24; b = -56; c = -160;
Δ = b2-4ac
Δ = -562-4·24·(-160)
Δ = 18496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18496}=136$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-136}{2*24}=\frac{-80}{48}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+136}{2*24}=\frac{192}{48}
=4
$