20=x^2/(3600-60x)

Solution for 20=x^2/(3600-60x) equation:

20=x^2/(3600-60x)

We move all terms to the left:

20-(x^2/(3600-60x))=0


Domain of the equation: (3600-60x))!=0

We move all terms containing x to the left, all other terms to the right

-60x)!=-3600

x!=-3600/1

x!=-3600

x∈R


We add all the numbers together, and all the variables

-(x^2/(-60x+3600))+20=0

We multiply all the terms by the denominator


-(x^2+20*(-60x+3600))=0


We calculate terms in parentheses: -(x^2+20*(-60x+3600)), so:

x^2+20*(-60x+3600)

We multiply parentheses

x^2-1200x+72000

Back to the equation:

-(x^2-1200x+72000)


We get rid of parentheses

-x^2+1200x-72000=0

We add all the numbers together, and all the variables

-1x^2+1200x-72000=0

a = -1; b = 1200; c = -72000;
Δ = b2-4ac
Δ = 12002-4·(-1)·(-72000)
Δ = 1152000
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:

$\sqrt{\Delta}=\sqrt{1152000}=\sqrt{230400*5}=\sqrt{230400}*\sqrt{5}=480\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-480\sqrt{5}}{2*-1}=\frac{-1200-480\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+480\sqrt{5}}{2*-1}=\frac{-1200+480\sqrt{5}}{-2}
$