5n^2-5n-1000=0

Solution for 5n^2-5n-1000=0 equation:

5n^2-5n-1000=0

a = 5; b = -5; c = -1000;
Δ = b2-4ac
Δ = -52-4·5·(-1000)
Δ = 20025
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:

$\sqrt{\Delta}=\sqrt{20025}=\sqrt{225*89}=\sqrt{225}*\sqrt{89}=15\sqrt{89}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15\sqrt{89}}{2*5}=\frac{5-15\sqrt{89}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15\sqrt{89}}{2*5}=\frac{5+15\sqrt{89}}{10}
$