2k^2=30-4k

Solution for 2k^2=30-4k equation:

2k^2=30-4k

We move all terms to the left:

2k^2-(30-4k)=0

We add all the numbers together, and all the variables

2k^2-(-4k+30)=0

We get rid of parentheses

2k^2+4k-30=0

a = 2; b = 4; c = -30;
Δ = b2-4ac
Δ = 42-4·2·(-30)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*2}=\frac{-20}{4}
=-5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*2}=\frac{12}{4}
=3
$