8k^2-10=-16k

Solution for 8k^2-10=-16k equation:

8k^2-10=-16k

We move all terms to the left:

8k^2-10-(-16k)=0

We get rid of parentheses

8k^2+16k-10=0

a = 8; b = 16; c = -10;
Δ = b2-4ac
Δ = 162-4·8·(-10)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24}{2*8}=\frac{-40}{16}
=-2+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24}{2*8}=\frac{8}{16}
=1/2
$