8k(k+6)=104

Solution for 8k(k+6)=104 equation:

8k(k+6)=104

We move all terms to the left:

8k(k+6)-(104)=0

We multiply parentheses

8k^2+48k-104=0

a = 8; b = 48; c = -104;
Δ = b2-4ac
Δ = 482-4·8·(-104)
Δ = 5632
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:

$\sqrt{\Delta}=\sqrt{5632}=\sqrt{256*22}=\sqrt{256}*\sqrt{22}=16\sqrt{22}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{22}}{2*8}=\frac{-48-16\sqrt{22}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{22}}{2*8}=\frac{-48+16\sqrt{22}}{16}
$