9(6c+7)c=3

Solution for 9(6c+7)c=3 equation:

9(6c+7)c=3

We move all terms to the left:

9(6c+7)c-(3)=0

We multiply parentheses

54c^2+63c-3=0

a = 54; b = 63; c = -3;
Δ = b2-4ac
Δ = 632-4·54·(-3)
Δ = 4617
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:

$\sqrt{\Delta}=\sqrt{4617}=\sqrt{81*57}=\sqrt{81}*\sqrt{57}=9\sqrt{57}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-9\sqrt{57}}{2*54}=\frac{-63-9\sqrt{57}}{108}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+9\sqrt{57}}{2*54}=\frac{-63+9\sqrt{57}}{108}
$