0=2x^2+13x-9

Solution for 0=2x^2+13x-9 equation:

0=2x^2+13x-9

We move all terms to the left:

0-(2x^2+13x-9)=0

We add all the numbers together, and all the variables

-(2x^2+13x-9)=0

We get rid of parentheses

-2x^2-13x+9=0

a = -2; b = -13; c = +9;
Δ = b2-4ac
Δ = -132-4·(-2)·9
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{241}}{2*-2}=\frac{13-\sqrt{241}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{241}}{2*-2}=\frac{13+\sqrt{241}}{-4}
$