6k^2-16=-8k

Solution for 6k^2-16=-8k equation:

6k^2-16=-8k

We move all terms to the left:

6k^2-16-(-8k)=0

We get rid of parentheses

6k^2+8k-16=0

a = 6; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·6·(-16)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{7}}{2*6}=\frac{-8-8\sqrt{7}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{7}}{2*6}=\frac{-8+8\sqrt{7}}{12}
$