9(c+6)c=7

Solution for 9(c+6)c=7 equation:

9(c+6)c=7

We move all terms to the left:

9(c+6)c-(7)=0

We multiply parentheses

9c^2+54c-7=0

a = 9; b = 54; c = -7;
Δ = b2-4ac
Δ = 542-4·9·(-7)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-12\sqrt{22}}{2*9}=\frac{-54-12\sqrt{22}}{18}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+12\sqrt{22}}{2*9}=\frac{-54+12\sqrt{22}}{18}
$