(2k-1)(3k-2)=330

Solution for (2k-1)(3k-2)=330 equation:

(2k-1)(3k-2)=330

We move all terms to the left:

(2k-1)(3k-2)-(330)=0

We multiply parentheses ..

(+6k^2-4k-3k+2)-330=0

We get rid of parentheses

6k^2-4k-3k+2-330=0

We add all the numbers together, and all the variables

6k^2-7k-328=0

a = 6; b = -7; c = -328;
Δ = b2-4ac
Δ = -72-4·6·(-328)
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-89}{2*6}=\frac{-82}{12}
=-6+5/6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+89}{2*6}=\frac{96}{12}
=8
$