(X+20)(x-40)=2700^2

Solution for (X+20)(x-40)=2700^2 equation:

(X+20)(X-40)=2700^2

We move all terms to the left:

(X+20)(X-40)-(2700^2)=0

We add all the numbers together, and all the variables

(X+20)(X-40)-7290000=0

We multiply parentheses ..

(+X^2-40X+20X-800)-7290000=0

We get rid of parentheses

X^2-40X+20X-800-7290000=0

We add all the numbers together, and all the variables

X^2-20X-7290800=0

a = 1; b = -20; c = -7290800;
Δ = b2-4ac
Δ = -202-4·1·(-7290800)
Δ = 29163600
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:

$\sqrt{\Delta}=\sqrt{29163600}=\sqrt{3600*8101}=\sqrt{3600}*\sqrt{8101}=60\sqrt{8101}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-60\sqrt{8101}}{2*1}=\frac{20-60\sqrt{8101}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+60\sqrt{8101}}{2*1}=\frac{20+60\sqrt{8101}}{2}
$