X^2-80x-75000=0

Solution for X^2-80x-75000=0 equation:

X^2-80X-75000=0

a = 1; b = -80; c = -75000;
Δ = b2-4ac
Δ = -802-4·1·(-75000)
Δ = 306400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{306400}=\sqrt{400*766}=\sqrt{400}*\sqrt{766}=20\sqrt{766}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{766}}{2*1}=\frac{80-20\sqrt{766}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{766}}{2*1}=\frac{80+20\sqrt{766}}{2}
$