5=x^2/(3000-60x)

Solution for 5=x^2/(3000-60x) equation:

5=x^2/(3000-60x)

We move all terms to the left:

5-(x^2/(3000-60x))=0


Domain of the equation: (3000-60x))!=0

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

-60x)!=-3000

x!=-3000/1

x!=-3000

x∈R


We add all the numbers together, and all the variables

-(x^2/(-60x+3000))+5=0

We multiply all the terms by the denominator


-(x^2+5*(-60x+3000))=0


We calculate terms in parentheses: -(x^2+5*(-60x+3000)), so:

x^2+5*(-60x+3000)

We multiply parentheses

x^2-300x+15000

Back to the equation:

-(x^2-300x+15000)


We get rid of parentheses

-x^2+300x-15000=0

We add all the numbers together, and all the variables

-1x^2+300x-15000=0

a = -1; b = 300; c = -15000;
Δ = b2-4ac
Δ = 3002-4·(-1)·(-15000)
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-100\sqrt{3}}{2*-1}=\frac{-300-100\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+100\sqrt{3}}{2*-1}=\frac{-300+100\sqrt{3}}{-2}
$