9c^2-12c-68=0

Solution for 9c^2-12c-68=0 equation:

9c^2-12c-68=0

a = 9; b = -12; c = -68;
Δ = b2-4ac
Δ = -122-4·9·(-68)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36\sqrt{2}}{2*9}=\frac{12-36\sqrt{2}}{18}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36\sqrt{2}}{2*9}=\frac{12+36\sqrt{2}}{18}
$