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

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

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

We move all terms to the left:

2700^2-((x+20)(x-40))=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 calculate terms in parentheses: -((+x^2-40x+20x-800)), so:

(+x^2-40x+20x-800)

We get rid of parentheses

x^2-40x+20x-800

We add all the numbers together, and all the variables

x^2-20x-800

Back to the equation:

-(x^2-20x-800)


We get rid of parentheses

-x^2+20x+800+7290000=0

We add all the numbers together, and all the variables

-1x^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}
$