3c^2-16c-20=-9

Solution for 3c^2-16c-20=-9 equation:

3c^2-16c-20=-9

We move all terms to the left:

3c^2-16c-20-(-9)=0

We add all the numbers together, and all the variables

3c^2-16c-11=0

a = 3; b = -16; c = -11;
Δ = b2-4ac
Δ = -162-4·3·(-11)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{97}}{2*3}=\frac{16-2\sqrt{97}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{97}}{2*3}=\frac{16+2\sqrt{97}}{6}
$