9(c-3)c=9

Solution for 9(c-3)c=9 equation:

9(c-3)c=9

We move all terms to the left:

9(c-3)c-(9)=0

We multiply parentheses

9c^2-27c-9=0

a = 9; b = -27; c = -9;
Δ = b2-4ac
Δ = -272-4·9·(-9)
Δ = 1053
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:

$\sqrt{\Delta}=\sqrt{1053}=\sqrt{81*13}=\sqrt{81}*\sqrt{13}=9\sqrt{13}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{13}}{2*9}=\frac{27-9\sqrt{13}}{18}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{13}}{2*9}=\frac{27+9\sqrt{13}}{18}
$