7k^2-16k=100

Solution for 7k^2-16k=100 equation:

7k^2-16k=100

We move all terms to the left:

7k^2-16k-(100)=0

a = 7; b = -16; c = -100;
Δ = b2-4ac
Δ = -162-4·7·(-100)
Δ = 3056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3056}=\sqrt{16*191}=\sqrt{16}*\sqrt{191}=4\sqrt{191}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{191}}{2*7}=\frac{16-4\sqrt{191}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{191}}{2*7}=\frac{16+4\sqrt{191}}{14}
$