c^2-6c=18

Solution for c^2-6c=18 equation:

c^2-6c=18

We move all terms to the left:

c^2-6c-(18)=0

a = 1; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·1·(-18)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*1}=\frac{6-6\sqrt{3}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*1}=\frac{6+6\sqrt{3}}{2}
$