1000-100x-16x^2=0

Solution for 1000-100x-16x^2=0 equation:

1000-100x-16x^2=0

a = -16; b = -100; c = +1000;
Δ = b2-4ac
Δ = -1002-4·(-16)·1000
Δ = 74000
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:

$\sqrt{\Delta}=\sqrt{74000}=\sqrt{400*185}=\sqrt{400}*\sqrt{185}=20\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{185}}{2*-16}=\frac{100-20\sqrt{185}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{185}}{2*-16}=\frac{100+20\sqrt{185}}{-32}
$