0=x^2-13x-40

Solution for 0=x^2-13x-40 equation:

0=x^2-13x-40

We move all terms to the left:

0-(x^2-13x-40)=0

We add all the numbers together, and all the variables

-(x^2-13x-40)=0

We get rid of parentheses

-x^2+13x+40=0

We add all the numbers together, and all the variables

-1x^2+13x+40=0

a = -1; b = 13; c = +40;
Δ = b2-4ac
Δ = 132-4·(-1)·40
Δ = 329
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{329}}{2*-1}=\frac{-13-\sqrt{329}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{329}}{2*-1}=\frac{-13+\sqrt{329}}{-2}
$