2k^2=33+5k

Solution for 2k^2=33+5k equation:

2k^2=33+5k

We move all terms to the left:

2k^2-(33+5k)=0

We add all the numbers together, and all the variables

2k^2-(5k+33)=0

We get rid of parentheses

2k^2-5k-33=0

a = 2; b = -5; c = -33;
Δ = b2-4ac
Δ = -52-4·2·(-33)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-17}{2*2}=\frac{-12}{4}
=-3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+17}{2*2}=\frac{22}{4}
=5+1/2
$