9k+5k(2)=38

Solution for 9k+5k(2)=38 equation:

9k+5k(2)=38

We move all terms to the left:

9k+5k(2)-(38)=0

We add all the numbers together, and all the variables

5k^2+9k-38=0

a = 5; b = 9; c = -38;
Δ = b2-4ac
Δ = 92-4·5·(-38)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-29}{2*5}=\frac{-38}{10}
=-3+4/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+29}{2*5}=\frac{20}{10}
=2
$