2k^2=-7-9k

Solution for 2k^2=-7-9k equation:

2k^2=-7-9k

We move all terms to the left:

2k^2-(-7-9k)=0

We add all the numbers together, and all the variables

2k^2-(-9k-7)=0

We get rid of parentheses

2k^2+9k+7=0

a = 2; b = 9; c = +7;
Δ = b2-4ac
Δ = 92-4·2·7
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5}{2*2}=\frac{-14}{4}
=-3+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*2}=\frac{-4}{4}
=-1
$