30+x=900/x

Solution for 30+x=900/x equation:

30+x=900/x

We move all terms to the left:

30+x-(900/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+900/x)+30=0

We get rid of parentheses

x-900/x+30=0

We multiply all the terms by the denominator


x*x+30*x-900=0

We add all the numbers together, and all the variables

30x+x*x-900=0

Wy multiply elements

x^2+30x-900=0

a = 1; b = 30; c = -900;
Δ = b2-4ac
Δ = 302-4·1·(-900)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{5}}{2*1}=\frac{-30-30\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{5}}{2*1}=\frac{-30+30\sqrt{5}}{2}
$