20/x=30-x

Solution for 20/x=30-x equation:

20/x=30-x

We move all terms to the left:

20/x-(30-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

20/x-(-1x+30)=0

We get rid of parentheses

20/x+1x-30=0

We multiply all the terms by the denominator


1x*x-30*x+20=0

We add all the numbers together, and all the variables

-30x+1x*x+20=0

Wy multiply elements

x^2-30x+20=0

a = 1; b = -30; c = +20;
Δ = b2-4ac
Δ = -302-4·1·20
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{205}}{2*1}=\frac{30-2\sqrt{205}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{205}}{2*1}=\frac{30+2\sqrt{205}}{2}
$