8(c+3)c=2

Solution for 8(c+3)c=2 equation:

8(c+3)c=2

We move all terms to the left:

8(c+3)c-(2)=0

We multiply parentheses

8c^2+24c-2=0

a = 8; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·8·(-2)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{10}}{2*8}=\frac{-24-8\sqrt{10}}{16}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{10}}{2*8}=\frac{-24+8\sqrt{10}}{16}
$