5n^2-40n-9600=0

Solution for 5n^2-40n-9600=0 equation:

5n^2-40n-9600=0

a = 5; b = -40; c = -9600;
Δ = b2-4ac
Δ = -402-4·5·(-9600)
Δ = 193600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{193600}=440$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-440}{2*5}=\frac{-400}{10}
=-40
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+440}{2*5}=\frac{480}{10}
=48
$