16k(k-5)=12K

Solution for 16k(k-5)=12K equation:

16k(k-5)=12

We move all terms to the left:

16k(k-5)-(12)=0

We multiply parentheses

16k^2-80k-12=0

a = 16; b = -80; c = -12;
Δ = b2-4ac
Δ = -802-4·16·(-12)
Δ = 7168
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:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-32\sqrt{7}}{2*16}=\frac{80-32\sqrt{7}}{32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+32\sqrt{7}}{2*16}=\frac{80+32\sqrt{7}}{32}
$