5=x^2/3600-60x

Solution for 5=x^2/3600-60x equation:

5=x^2/3600-60x

We move all terms to the left:

5-(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 get rid of parentheses

-x^2/3600+60x+5=0

We multiply all the terms by the denominator


-x^2+60x*3600+5*3600=0

We add all the numbers together, and all the variables

-1x^2+60x*3600+18000=0

Wy multiply elements

-1x^2+216000x+18000=0

a = -1; b = 216000; c = +18000;
Δ = b2-4ac
Δ = 2160002-4·(-1)·18000
Δ = 46656072000
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:

$\sqrt{\Delta}=\sqrt{46656072000}=\sqrt{14400*3240005}=\sqrt{14400}*\sqrt{3240005}=120\sqrt{3240005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216000)-120\sqrt{3240005}}{2*-1}=\frac{-216000-120\sqrt{3240005}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216000)+120\sqrt{3240005}}{2*-1}=\frac{-216000+120\sqrt{3240005}}{-2}
$