44=5(3k+2)2k

Solution for 44=5(3k+2)2k equation:

44=5(3k+2)2k

We move all terms to the left:

44-(5(3k+2)2k)=0


We calculate terms in parentheses: -(5(3k+2)2k), so:

5(3k+2)2k

We multiply parentheses

30k^2+20k

Back to the equation:

-(30k^2+20k)


We get rid of parentheses

-30k^2-20k+44=0

a = -30; b = -20; c = +44;
Δ = b2-4ac
Δ = -202-4·(-30)·44
Δ = 5680
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:

$\sqrt{\Delta}=\sqrt{5680}=\sqrt{16*355}=\sqrt{16}*\sqrt{355}=4\sqrt{355}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{355}}{2*-30}=\frac{20-4\sqrt{355}}{-60}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{355}}{2*-30}=\frac{20+4\sqrt{355}}{-60}
$