6+9z+z2=0

Solution for 6+9z+z2=0 equation:

6+9z+z2=0

We add all the numbers together, and all the variables

z^2+9z+6=0

a = 1; b = 9; c = +6;
Δ = b2-4ac
Δ = 92-4·1·6
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{57}}{2*1}=\frac{-9-\sqrt{57}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*1}=\frac{-9+\sqrt{57}}{2}
$