6k^2-42k=72=0

Solution for 6k^2-42k=72=0 equation:

6k^2-42k=72=0

We move all terms to the left:

6k^2-42k-(72)=0

a = 6; b = -42; c = -72;
Δ = b2-4ac
Δ = -422-4·6·(-72)
Δ = 3492
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:

$\sqrt{\Delta}=\sqrt{3492}=\sqrt{36*97}=\sqrt{36}*\sqrt{97}=6\sqrt{97}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{97}}{2*6}=\frac{42-6\sqrt{97}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{97}}{2*6}=\frac{42+6\sqrt{97}}{12}
$