8k^2+40k=192

Solution for 8k^2+40k=192 equation:

8k^2+40k=192

We move all terms to the left:

8k^2+40k-(192)=0

a = 8; b = 40; c = -192;
Δ = b2-4ac
Δ = 402-4·8·(-192)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-88}{2*8}=\frac{-128}{16}
=-8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+88}{2*8}=\frac{48}{16}
=3
$