(20k+4)(33k-9)=360

Solution for (20k+4)(33k-9)=360 equation:

(20k+4)(33k-9)=360

We move all terms to the left:

(20k+4)(33k-9)-(360)=0

We multiply parentheses ..

(+660k^2-180k+132k-36)-360=0

We get rid of parentheses

660k^2-180k+132k-36-360=0

We add all the numbers together, and all the variables

660k^2-48k-396=0

a = 660; b = -48; c = -396;
Δ = b2-4ac
Δ = -482-4·660·(-396)
Δ = 1047744
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:

$\sqrt{\Delta}=\sqrt{1047744}=\sqrt{576*1819}=\sqrt{576}*\sqrt{1819}=24\sqrt{1819}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{1819}}{2*660}=\frac{48-24\sqrt{1819}}{1320}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{1819}}{2*660}=\frac{48+24\sqrt{1819}}{1320}
$