7(x+2)(x-40)=-2

Solution for 7(x+2)(x-40)=-2 equation:

7(x+2)(x-40)=-2

We move all terms to the left:

7(x+2)(x-40)-(-2)=0

We add all the numbers together, and all the variables

7(x+2)(x-40)+2=0

We multiply parentheses ..

7(+x^2-40x+2x-80)+2=0

We multiply parentheses

7x^2-280x+14x-560+2=0

We add all the numbers together, and all the variables

7x^2-266x-558=0

a = 7; b = -266; c = -558;
Δ = b2-4ac
Δ = -2662-4·7·(-558)
Δ = 86380
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:

$\sqrt{\Delta}=\sqrt{86380}=\sqrt{4*21595}=\sqrt{4}*\sqrt{21595}=2\sqrt{21595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-266)-2\sqrt{21595}}{2*7}=\frac{266-2\sqrt{21595}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-266)+2\sqrt{21595}}{2*7}=\frac{266+2\sqrt{21595}}{14}
$