(6k-48)(-4-12k)=-52

Solution for (6k-48)(-4-12k)=-52 equation:

(6k-48)(-4-12k)=-52

We move all terms to the left:

(6k-48)(-4-12k)-(-52)=0

We add all the numbers together, and all the variables

(6k-48)(-12k-4)-(-52)=0

We add all the numbers together, and all the variables

(6k-48)(-12k-4)+52=0

We multiply parentheses ..

(-72k^2-24k+576k+192)+52=0

We get rid of parentheses

-72k^2-24k+576k+192+52=0

We add all the numbers together, and all the variables

-72k^2+552k+244=0

a = -72; b = 552; c = +244;
Δ = b2-4ac
Δ = 5522-4·(-72)·244
Δ = 374976
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:

$\sqrt{\Delta}=\sqrt{374976}=\sqrt{576*651}=\sqrt{576}*\sqrt{651}=24\sqrt{651}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(552)-24\sqrt{651}}{2*-72}=\frac{-552-24\sqrt{651}}{-144}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(552)+24\sqrt{651}}{2*-72}=\frac{-552+24\sqrt{651}}{-144}
$