c^2-3c=27+3c

Solution for c^2-3c=27+3c equation:

c^2-3c=27+3c

We move all terms to the left:

c^2-3c-(27+3c)=0

We add all the numbers together, and all the variables

c^2-3c-(3c+27)=0

We get rid of parentheses

c^2-3c-3c-27=0

We add all the numbers together, and all the variables

c^2-6c-27=0

a = 1; b = -6; c = -27;
Δ = b2-4ac
Δ = -62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*1}=\frac{-6}{2}
=-3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*1}=\frac{18}{2}
=9
$