6c^2-17c+7=0

Solution for 6c^2-17c+7=0 equation:

6c^2-17c+7=0

a = 6; b = -17; c = +7;
Δ = b2-4ac
Δ = -172-4·6·7
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-11}{2*6}=\frac{6}{12}
=1/2
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+11}{2*6}=\frac{28}{12}
=2+1/3
$