(x+18)(x+20)=20

Solution for (x+18)(x+20)=20 equation:

(x+18)(x+20)=20

We move all terms to the left:

(x+18)(x+20)-(20)=0

We multiply parentheses ..

(+x^2+20x+18x+360)-20=0

We get rid of parentheses

x^2+20x+18x+360-20=0

We add all the numbers together, and all the variables

x^2+38x+340=0

a = 1; b = 38; c = +340;
Δ = b2-4ac
Δ = 382-4·1·340
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{21}}{2*1}=\frac{-38-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{21}}{2*1}=\frac{-38+2\sqrt{21}}{2}
$