9k=+k2+9=31

Solution for 9k=+k2+9=31 equation:

9k=+k2+9=31

We move all terms to the left:

9k-(+k2+9)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-k^2+9k-9=0

We add all the numbers together, and all the variables

-1k^2+9k-9=0

a = -1; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·(-1)·(-9)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*-1}=\frac{-9-3\sqrt{5}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*-1}=\frac{-9+3\sqrt{5}}{-2}
$