6k^2-42k+71=0

Solution for 6k^2-42k+71=0 equation:

6k^2-42k+71=0

a = 6; b = -42; c = +71;
Δ = b2-4ac
Δ = -422-4·6·71
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{15}}{2*6}=\frac{42-2\sqrt{15}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{15}}{2*6}=\frac{42+2\sqrt{15}}{12}
$