(2x-50)(x+20)=1

Solution for (2x-50)(x+20)=1 equation:

(2x-50)(x+20)=1

We move all terms to the left:

(2x-50)(x+20)-(1)=0

We multiply parentheses ..

(+2x^2+40x-50x-1000)-1=0

We get rid of parentheses

2x^2+40x-50x-1000-1=0

We add all the numbers together, and all the variables

2x^2-10x-1001=0

a = 2; b = -10; c = -1001;
Δ = b2-4ac
Δ = -102-4·2·(-1001)
Δ = 8108
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:

$\sqrt{\Delta}=\sqrt{8108}=\sqrt{4*2027}=\sqrt{4}*\sqrt{2027}=2\sqrt{2027}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{2027}}{2*2}=\frac{10-2\sqrt{2027}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{2027}}{2*2}=\frac{10+2\sqrt{2027}}{4}
$