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 get rid of parentheses

2k^2+9k-7=0

a = 2; b = 9; c = -7;
Δ = b2-4ac
Δ = 92-4·2·(-7)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{137}}{2*2}=\frac{-9-\sqrt{137}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{137}}{2*2}=\frac{-9+\sqrt{137}}{4}
$