600=600/x+1.5*x

Solution for 600=600/x+1.5*x equation:

600=600/x+1.5x

We move all terms to the left:

600-(600/x+1.5x)=0


Domain of the equation: x+1.5x)!=0

x∈R


We add all the numbers together, and all the variables

-(+1.5x+600/x)+600=0

We get rid of parentheses

-1.5x-600/x+600=0

We multiply all the terms by the denominator


-(1.5x)*x+600*x-600=0

We add all the numbers together, and all the variables

-(+1.5x)*x+600*x-600=0

We add all the numbers together, and all the variables

600x-(+1.5x)*x-600=0

We multiply parentheses

-x^2+600x-600=0

We add all the numbers together, and all the variables

-1x^2+600x-600=0

a = -1; b = 600; c = -600;
Δ = b2-4ac
Δ = 6002-4·(-1)·(-600)
Δ = 357600
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:

$\sqrt{\Delta}=\sqrt{357600}=\sqrt{400*894}=\sqrt{400}*\sqrt{894}=20\sqrt{894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-20\sqrt{894}}{2*-1}=\frac{-600-20\sqrt{894}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+20\sqrt{894}}{2*-1}=\frac{-600+20\sqrt{894}}{-2}
$