3k^2-34k+11=0

Solution for 3k^2-34k+11=0 equation:

3k^2-34k+11=0

a = 3; b = -34; c = +11;
Δ = b2-4ac
Δ = -342-4·3·11
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-32}{2*3}=\frac{2}{6}
=1/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+32}{2*3}=\frac{66}{6}
=11
$