0=x^2+10x-119

Solution for 0=x^2+10x-119 equation:

0=x^2+10x-119

We move all terms to the left:

0-(x^2+10x-119)=0

We add all the numbers together, and all the variables

-(x^2+10x-119)=0

We get rid of parentheses

-x^2-10x+119=0

We add all the numbers together, and all the variables

-1x^2-10x+119=0

a = -1; b = -10; c = +119;
Δ = b2-4ac
Δ = -102-4·(-1)·119
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-24}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+24}{2*-1}=\frac{34}{-2}
=-17
$