X^2+80x-38500=0

Solution for X^2+80x-38500=0 equation:

X^2+80X-38500=0

a = 1; b = 80; c = -38500;
Δ = b2-4ac
Δ = 802-4·1·(-38500)
Δ = 160400
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:

$\sqrt{\Delta}=\sqrt{160400}=\sqrt{400*401}=\sqrt{400}*\sqrt{401}=20\sqrt{401}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{401}}{2*1}=\frac{-80-20\sqrt{401}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{401}}{2*1}=\frac{-80+20\sqrt{401}}{2}
$