6z^2-18z-18=6

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

6z^2-18z-18=6

We move all terms to the left:

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

We add all the numbers together, and all the variables

6z^2-18z-24=0

a = 6; b = -18; c = -24;
Δ = b2-4ac
Δ = -182-4·6·(-24)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30}{2*6}=\frac{-12}{12}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*6}=\frac{48}{12}
=4
$