(12*x+(12*x)/x)+120*4/x=600

Solution for (12*x+(12*x)/x)+120*4/x=600 equation:

(12x+(12x)/x)+120*4/x=600

We move all terms to the left:

(12x+(12x)/x)+120*4/x-(600)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(+12x+12x/x)+120*4/x-600=0

We get rid of parentheses

12x+12x/x+120*4/x-600=0

We multiply all the terms by the denominator


12x*x+12x-600*x+120*4=0

We add all the numbers together, and all the variables

-588x+12x*x+480=0

Wy multiply elements

12x^2-588x+480=0

a = 12; b = -588; c = +480;
Δ = b2-4ac
Δ = -5882-4·12·480
Δ = 322704
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:

$\sqrt{\Delta}=\sqrt{322704}=\sqrt{1296*249}=\sqrt{1296}*\sqrt{249}=36\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-588)-36\sqrt{249}}{2*12}=\frac{588-36\sqrt{249}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-588)+36\sqrt{249}}{2*12}=\frac{588+36\sqrt{249}}{24}
$