(x+20)(x-100)=14

Solution for (x+20)(x-100)=14 equation:

(x+20)(x-100)=14

We move all terms to the left:

(x+20)(x-100)-(14)=0

We multiply parentheses ..

(+x^2-100x+20x-2000)-14=0

We get rid of parentheses

x^2-100x+20x-2000-14=0

We add all the numbers together, and all the variables

x^2-80x-2014=0

a = 1; b = -80; c = -2014;
Δ = b2-4ac
Δ = -802-4·1·(-2014)
Δ = 14456
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:

$\sqrt{\Delta}=\sqrt{14456}=\sqrt{4*3614}=\sqrt{4}*\sqrt{3614}=2\sqrt{3614}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{3614}}{2*1}=\frac{80-2\sqrt{3614}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{3614}}{2*1}=\frac{80+2\sqrt{3614}}{2}
$