(7x-7)(x+14)=180

Solution for (7x-7)(x+14)=180 equation:

(7x-7)(x+14)=180

We move all terms to the left:

(7x-7)(x+14)-(180)=0

We multiply parentheses ..

(+7x^2+98x-7x-98)-180=0

We get rid of parentheses

7x^2+98x-7x-98-180=0

We add all the numbers together, and all the variables

7x^2+91x-278=0

a = 7; b = 91; c = -278;
Δ = b2-4ac
Δ = 912-4·7·(-278)
Δ = 16065
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:

$\sqrt{\Delta}=\sqrt{16065}=\sqrt{9*1785}=\sqrt{9}*\sqrt{1785}=3\sqrt{1785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-3\sqrt{1785}}{2*7}=\frac{-91-3\sqrt{1785}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+3\sqrt{1785}}{2*7}=\frac{-91+3\sqrt{1785}}{14}
$