X^2-16x-3000=0

Solution for X^2-16x-3000=0 equation:

X^2-16X-3000=0

a = 1; b = -16; c = -3000;
Δ = b2-4ac
Δ = -162-4·1·(-3000)
Δ = 12256
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:

$\sqrt{\Delta}=\sqrt{12256}=\sqrt{16*766}=\sqrt{16}*\sqrt{766}=4\sqrt{766}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{766}}{2*1}=\frac{16-4\sqrt{766}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{766}}{2*1}=\frac{16+4\sqrt{766}}{2}
$