0=2x^2+13x+6

Solution for 0=2x^2+13x+6 equation:

0=2x^2+13x+6

We move all terms to the left:

0-(2x^2+13x+6)=0

We add all the numbers together, and all the variables

-(2x^2+13x+6)=0

We get rid of parentheses

-2x^2-13x-6=0

a = -2; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·(-2)·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*-2}=\frac{2}{-4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*-2}=\frac{24}{-4}
=-6
$