3a^2=-11a-6

Solution for 3a^2=-11a-6 equation:

3a^2=-11a-6

We move all terms to the left:

3a^2-(-11a-6)=0

We get rid of parentheses

3a^2+11a+6=0

a = 3; b = 11; c = +6;
Δ = b2-4ac
Δ = 112-4·3·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*3}=\frac{-18}{6}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*3}=\frac{-4}{6}
=-2/3
$