8n^2+4008n-83500=0

Solution for 8n^2+4008n-83500=0 equation:

8n^2+4008n-83500=0

a = 8; b = 4008; c = -83500;
Δ = b2-4ac
Δ = 40082-4·8·(-83500)
Δ = 18736064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18736064}=\sqrt{64*292751}=\sqrt{64}*\sqrt{292751}=8\sqrt{292751}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4008)-8\sqrt{292751}}{2*8}=\frac{-4008-8\sqrt{292751}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4008)+8\sqrt{292751}}{2*8}=\frac{-4008+8\sqrt{292751}}{16}
$