6c=9c^2

Solution for 6c=9c^2 equation:

6c=9c^2

We move all terms to the left:

6c-(9c^2)=0

determiningTheFunctionDomain
-9c^2+6c=0

a = -9; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-9)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-9}=\frac{-12}{-18}
=2/3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-9}=\frac{0}{-18}
=0
$