1000=16k^2-k

Solution for 1000=16k^2-k equation:

1000=16k^2-k

We move all terms to the left:

1000-(16k^2-k)=0

We get rid of parentheses

-16k^2+k+1000=0

a = -16; b = 1; c = +1000;
Δ = b2-4ac
Δ = 12-4·(-16)·1000
Δ = 64001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{64001}}{2*-16}=\frac{-1-\sqrt{64001}}{-32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{64001}}{2*-16}=\frac{-1+\sqrt{64001}}{-32}
$