9c^2-4c-52=0

Solution for 9c^2-4c-52=0 equation:

9c^2-4c-52=0

a = 9; b = -4; c = -52;
Δ = b2-4ac
Δ = -42-4·9·(-52)
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{118}}{2*9}=\frac{4-4\sqrt{118}}{18}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{118}}{2*9}=\frac{4+4\sqrt{118}}{18}
$