3/x+x+30=600

Solution for 3/x+x+30=600 equation:

3/x+x+30=600

We move all terms to the left:

3/x+x+30-(600)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x-570=0

We multiply all the terms by the denominator


x*x-570*x+3=0

We add all the numbers together, and all the variables

-570x+x*x+3=0

Wy multiply elements

x^2-570x+3=0

a = 1; b = -570; c = +3;
Δ = b2-4ac
Δ = -5702-4·1·3
Δ = 324888
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:

$\sqrt{\Delta}=\sqrt{324888}=\sqrt{4*81222}=\sqrt{4}*\sqrt{81222}=2\sqrt{81222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-570)-2\sqrt{81222}}{2*1}=\frac{570-2\sqrt{81222}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-570)+2\sqrt{81222}}{2*1}=\frac{570+2\sqrt{81222}}{2}
$