6k^2=42-9k

Solution for 6k^2=42-9k equation:

6k^2=42-9k

We move all terms to the left:

6k^2-(42-9k)=0

We add all the numbers together, and all the variables

6k^2-(-9k+42)=0

We get rid of parentheses

6k^2+9k-42=0

a = 6; b = 9; c = -42;
Δ = b2-4ac
Δ = 92-4·6·(-42)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-33}{2*6}=\frac{-42}{12}
=-3+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+33}{2*6}=\frac{24}{12}
=2
$