-j^2-9j-9=0

Solution for -j^2-9j-9=0 equation:

-j^2-9j-9=0

We add all the numbers together, and all the variables

-1j^2-9j-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:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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