3c^2+2c-34=0

Solution for 3c^2+2c-34=0 equation:

3c^2+2c-34=0

a = 3; b = 2; c = -34;
Δ = b2-4ac
Δ = 22-4·3·(-34)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{103}}{2*3}=\frac{-2-2\sqrt{103}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{103}}{2*3}=\frac{-2+2\sqrt{103}}{6}
$