150=x-30/x*600

Solution for 150=x-30/x*600 equation:

150=x-30/x*600

We move all terms to the left:

150-(x-30/x*600)=0


Domain of the equation: x*600)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-30/x*600)+150=0

We get rid of parentheses

-x+30/x*600+150=0

We multiply all the terms by the denominator


-x*x*600+150*x*600+30=0

Wy multiply elements

-600x^2*6+90000x*6+30=0

Wy multiply elements

-3600x^2+540000x+30=0

a = -3600; b = 540000; c = +30;
Δ = b2-4ac
Δ = 5400002-4·(-3600)·30
Δ = 291600432000
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:

$\sqrt{\Delta}=\sqrt{291600432000}=\sqrt{14400*20250030}=\sqrt{14400}*\sqrt{20250030}=120\sqrt{20250030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540000)-120\sqrt{20250030}}{2*-3600}=\frac{-540000-120\sqrt{20250030}}{-7200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540000)+120\sqrt{20250030}}{2*-3600}=\frac{-540000+120\sqrt{20250030}}{-7200}
$