-c(6c+7)=0

Solution for -c(6c+7)=0 equation:

-c(6c+7)=0

We multiply parentheses

-6c^2-7c=0

a = -6; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-6)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-6}=\frac{0}{-12}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-6}=\frac{14}{-12}
=-1+1/6
$