500n2+1500n-11000=0

Solution for 500n2+1500n-11000=0 equation:

500n^2+1500n-11000=0

a = 500; b = 1500; c = -11000;
Δ = b2-4ac
Δ = 15002-4·500·(-11000)
Δ = 24250000
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:

$\sqrt{\Delta}=\sqrt{24250000}=\sqrt{250000*97}=\sqrt{250000}*\sqrt{97}=500\sqrt{97}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1500)-500\sqrt{97}}{2*500}=\frac{-1500-500\sqrt{97}}{1000}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1500)+500\sqrt{97}}{2*500}=\frac{-1500+500\sqrt{97}}{1000}
$