0=x2+14x-80

Solution for 0=x2+14x-80 equation:

0=x2+14x-80

We move all terms to the left:

0-(x2+14x-80)=0

We add all the numbers together, and all the variables

-(+x^2+14x-80)+0=0

We add all the numbers together, and all the variables

-(+x^2+14x-80)=0

We get rid of parentheses

-x^2-14x+80=0

We add all the numbers together, and all the variables

-1x^2-14x+80=0

a = -1; b = -14; c = +80;
Δ = b2-4ac
Δ = -142-4·(-1)·80
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{129}}{2*-1}=\frac{14-2\sqrt{129}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{129}}{2*-1}=\frac{14+2\sqrt{129}}{-2}
$