3k^2-30k+22=0

Solution for 3k^2-30k+22=0 equation:

3k^2-30k+22=0

a = 3; b = -30; c = +22;
Δ = b2-4ac
Δ = -302-4·3·22
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{159}}{2*3}=\frac{30-2\sqrt{159}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{159}}{2*3}=\frac{30+2\sqrt{159}}{6}
$