n^2-75n-3000=0

Solution for n^2-75n-3000=0 equation:

n^2-75n-3000=0

a = 1; b = -75; c = -3000;
Δ = b2-4ac
Δ = -752-4·1·(-3000)
Δ = 17625
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:

$\sqrt{\Delta}=\sqrt{17625}=\sqrt{25*705}=\sqrt{25}*\sqrt{705}=5\sqrt{705}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{705}}{2*1}=\frac{75-5\sqrt{705}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{705}}{2*1}=\frac{75+5\sqrt{705}}{2}
$