6c2+4c-17=0

Solution for 6c2+4c-17=0 equation:

6c^2+4c-17=0

a = 6; b = 4; c = -17;
Δ = b2-4ac
Δ = 42-4·6·(-17)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{106}}{2*6}=\frac{-4-2\sqrt{106}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{106}}{2*6}=\frac{-4+2\sqrt{106}}{12}
$