4k^2-k=138

Solution for 4k^2-k=138 equation:

4k^2-k=138

We move all terms to the left:

4k^2-k-(138)=0

We add all the numbers together, and all the variables

4k^2-1k-138=0

a = 4; b = -1; c = -138;
Δ = b2-4ac
Δ = -12-4·4·(-138)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-47}{2*4}=\frac{-46}{8}
=-5+3/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+47}{2*4}=\frac{48}{8}
=6
$