0=6a^2+19a+6

Solution for 0=6a^2+19a+6 equation:

0=6a^2+19a+6

We move all terms to the left:

0-(6a^2+19a+6)=0

We add all the numbers together, and all the variables

-(6a^2+19a+6)=0

We get rid of parentheses

-6a^2-19a-6=0

a = -6; b = -19; c = -6;
Δ = b2-4ac
Δ = -192-4·(-6)·(-6)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{217}}{2*-6}=\frac{19-\sqrt{217}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{217}}{2*-6}=\frac{19+\sqrt{217}}{-12}
$