0=13x^2-4x-9

Solution for 0=13x^2-4x-9 equation:

0=13x^2-4x-9

We move all terms to the left:

0-(13x^2-4x-9)=0

We add all the numbers together, and all the variables

-(13x^2-4x-9)=0

We get rid of parentheses

-13x^2+4x+9=0

a = -13; b = 4; c = +9;
Δ = b2-4ac
Δ = 42-4·(-13)·9
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-22}{2*-13}=\frac{-26}{-26}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+22}{2*-13}=\frac{18}{-26}
=-9/13
$