c+7=-3c*(c+11)

Solution for c+7=-3c*(c+11) equation:

c+7=-3c*(c+11)

We move all terms to the left:

c+7-(-3c*(c+11))=0


We calculate terms in parentheses: -(-3c*(c+11)), so:

-3c*(c+11)

We multiply parentheses

-3c^2-33c

Back to the equation:

-(-3c^2-33c)


We get rid of parentheses

3c^2+33c+c+7=0

We add all the numbers together, and all the variables

3c^2+34c+7=0

a = 3; b = 34; c = +7;
Δ = b2-4ac
Δ = 342-4·3·7
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-4\sqrt{67}}{2*3}=\frac{-34-4\sqrt{67}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+4\sqrt{67}}{2*3}=\frac{-34+4\sqrt{67}}{6}
$