0=6k^2+15k+3

Solution for 0=6k^2+15k+3 equation:

0=6k^2+15k+3

We move all terms to the left:

0-(6k^2+15k+3)=0

We add all the numbers together, and all the variables

-(6k^2+15k+3)=0

We get rid of parentheses

-6k^2-15k-3=0

a = -6; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·(-6)·(-3)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{17}}{2*-6}=\frac{15-3\sqrt{17}}{-12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{17}}{2*-6}=\frac{15+3\sqrt{17}}{-12}
$