0=3x^2+16x+13

Solution for 0=3x^2+16x+13 equation:

0=3x^2+16x+13

We move all terms to the left:

0-(3x^2+16x+13)=0

We add all the numbers together, and all the variables

-(3x^2+16x+13)=0

We get rid of parentheses

-3x^2-16x-13=0

a = -3; b = -16; c = -13;
Δ = b2-4ac
Δ = -162-4·(-3)·(-13)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10}{2*-3}=\frac{6}{-6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10}{2*-3}=\frac{26}{-6}
=-4+1/3
$