0=3x^2+44x+65

Solution for 0=3x^2+44x+65 equation:

0=3x^2+44x+65

We move all terms to the left:

0-(3x^2+44x+65)=0

We add all the numbers together, and all the variables

-(3x^2+44x+65)=0

We get rid of parentheses

-3x^2-44x-65=0

a = -3; b = -44; c = -65;
Δ = b2-4ac
Δ = -442-4·(-3)·(-65)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-34}{2*-3}=\frac{10}{-6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+34}{2*-3}=\frac{78}{-6}
=-13
$