z^2-18z=-6

Solution for z^2-18z=-6 equation:

z^2-18z=-6

We move all terms to the left:

z^2-18z-(-6)=0

We add all the numbers together, and all the variables

z^2-18z+6=0

a = 1; b = -18; c = +6;
Δ = b2-4ac
Δ = -182-4·1·6
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*1}=\frac{18-10\sqrt{3}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*1}=\frac{18+10\sqrt{3}}{2}
$