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-630=0

We multiply all the terms by the denominator


x*x-630*x+3=0

We add all the numbers together, and all the variables

-630x+x*x+3=0

Wy multiply elements

x^2-630x+3=0

a = 1; b = -630; c = +3;
Δ = b2-4ac
Δ = -6302-4·1·3
Δ = 396888
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:

$\sqrt{\Delta}=\sqrt{396888}=\sqrt{4*99222}=\sqrt{4}*\sqrt{99222}=2\sqrt{99222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99222}}{2*1}=\frac{630-2\sqrt{99222}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99222}}{2*1}=\frac{630+2\sqrt{99222}}{2}
$