6(c+7)c=9

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

6(c+7)c=9

We move all terms to the left:

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

We multiply parentheses

6c^2+42c-9=0

a = 6; b = 42; c = -9;
Δ = b2-4ac
Δ = 422-4·6·(-9)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{55}}{2*6}=\frac{-42-6\sqrt{55}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{55}}{2*6}=\frac{-42+6\sqrt{55}}{12}
$