3k^2-k-14=0

Solution for 3k^2-k-14=0 equation:

3k^2-k-14=0

We add all the numbers together, and all the variables

3k^2-1k-14=0

a = 3; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·3·(-14)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*3}=\frac{-12}{6}
=-2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*3}=\frac{14}{6}
=2+1/3
$