8(c-3)c=9

Solution for 8(c-3)c=9 equation:

8(c-3)c=9

We move all terms to the left:

8(c-3)c-(9)=0

We multiply parentheses

8c^2-24c-9=0

a = 8; b = -24; c = -9;
Δ = b2-4ac
Δ = -242-4·8·(-9)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{6}}{2*8}=\frac{24-12\sqrt{6}}{16}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{6}}{2*8}=\frac{24+12\sqrt{6}}{16}
$