2k(2+3k)5=44

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

2k(2+3k)5=44

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply 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}
$