3c^2+2c=9

Solution for 3c^2+2c=9 equation:

3c^2+2c=9

We move all terms to the left:

3c^2+2c-(9)=0

a = 3; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·3·(-9)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{7}}{2*3}=\frac{-2-4\sqrt{7}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{7}}{2*3}=\frac{-2+4\sqrt{7}}{6}
$