6z(3z+3)=10+8

Solution for 6z(3z+3)=10+8 equation:

6z(3z+3)=10+8

We move all terms to the left:

6z(3z+3)-(10+8)=0

We add all the numbers together, and all the variables

6z(3z+3)-18=0

We multiply parentheses

18z^2+18z-18=0

a = 18; b = 18; c = -18;
Δ = b2-4ac
Δ = 182-4·18·(-18)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{5}}{2*18}=\frac{-18-18\sqrt{5}}{36}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{5}}{2*18}=\frac{-18+18\sqrt{5}}{36}
$