0=x^2-5x-22

Solution for 0=x^2-5x-22 equation:

0=x^2-5x-22

We move all terms to the left:

0-(x^2-5x-22)=0

We add all the numbers together, and all the variables

-(x^2-5x-22)=0

We get rid of parentheses

-x^2+5x+22=0

We add all the numbers together, and all the variables

-1x^2+5x+22=0

a = -1; b = 5; c = +22;
Δ = b2-4ac
Δ = 52-4·(-1)·22
Δ = 113
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{-(5)-\sqrt{113}}{2*-1}=\frac{-5-\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{113}}{2*-1}=\frac{-5+\sqrt{113}}{-2}
$