8c(c+3)=12

Solution for 8c(c+3)=12 equation:

8c(c+3)=12

We move all terms to the left:

8c(c+3)-(12)=0

We multiply parentheses

8c^2+24c-12=0

a = 8; b = 24; c = -12;
Δ = b2-4ac
Δ = 242-4·8·(-12)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{15}}{2*8}=\frac{-24-8\sqrt{15}}{16}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{15}}{2*8}=\frac{-24+8\sqrt{15}}{16}
$