6m^2+69m+33=0

Solution for 6m^2+69m+33=0 equation:

6m^2+69m+33=0

a = 6; b = 69; c = +33;
Δ = b2-4ac
Δ = 692-4·6·33
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-63}{2*6}=\frac{-132}{12}
=-11
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+63}{2*6}=\frac{-6}{12}
=-1/2
$