X^2-80x-68000=0

Solution for X^2-80x-68000=0 equation:

X^2-80X-68000=0

a = 1; b = -80; c = -68000;
Δ = b2-4ac
Δ = -802-4·1·(-68000)
Δ = 278400
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:

$\sqrt{\Delta}=\sqrt{278400}=\sqrt{1600*174}=\sqrt{1600}*\sqrt{174}=40\sqrt{174}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{174}}{2*1}=\frac{80-40\sqrt{174}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{174}}{2*1}=\frac{80+40\sqrt{174}}{2}
$