0=x^2+7x-119

Solution for 0=x^2+7x-119 equation:

0=x^2+7x-119

We move all terms to the left:

0-(x^2+7x-119)=0

We add all the numbers together, and all the variables

-(x^2+7x-119)=0

We get rid of parentheses

-x^2-7x+119=0

We add all the numbers together, and all the variables

-1x^2-7x+119=0

a = -1; b = -7; c = +119;
Δ = b2-4ac
Δ = -72-4·(-1)·119
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5\sqrt{21}}{2*-1}=\frac{7-5\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5\sqrt{21}}{2*-1}=\frac{7+5\sqrt{21}}{-2}
$