0=x^2+24x-191

Solution for 0=x^2+24x-191 equation:

0=x^2+24x-191

We move all terms to the left:

0-(x^2+24x-191)=0

We add all the numbers together, and all the variables

-(x^2+24x-191)=0

We get rid of parentheses

-x^2-24x+191=0

We add all the numbers together, and all the variables

-1x^2-24x+191=0

a = -1; b = -24; c = +191;
Δ = b2-4ac
Δ = -242-4·(-1)·191
Δ = 1340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1340}=\sqrt{4*335}=\sqrt{4}*\sqrt{335}=2\sqrt{335}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{335}}{2*-1}=\frac{24-2\sqrt{335}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{335}}{2*-1}=\frac{24+2\sqrt{335}}{-2}
$