0=x*x+14x-180

Solution for 0=x*x+14x-180 equation:

0=x*x+14x-180

We move all terms to the left:

0-(x*x+14x-180)=0

We add all the numbers together, and all the variables

-(14x+x*x-180)+0=0

We add all the numbers together, and all the variables

-(14x+x*x-180)=0

We get rid of parentheses

-14x-x*x+180=0

Wy multiply elements

-1x^2-14x+180=0

a = -1; b = -14; c = +180;
Δ = b2-4ac
Δ = -142-4·(-1)·180
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{229}}{2*-1}=\frac{14-2\sqrt{229}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{229}}{2*-1}=\frac{14+2\sqrt{229}}{-2}
$