9c(c-2)=18

Solution for 9c(c-2)=18 equation:

9c(c-2)=18

We move all terms to the left:

9c(c-2)-(18)=0

We multiply parentheses

9c^2-18c-18=0

a = 9; b = -18; c = -18;
Δ = b2-4ac
Δ = -182-4·9·(-18)
Δ = 972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{3}}{2*9}=\frac{18-18\sqrt{3}}{18}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{3}}{2*9}=\frac{18+18\sqrt{3}}{18}
$