30/x=40-x

Solution for 30/x=40-x equation:

30/x=40-x

We move all terms to the left:

30/x-(40-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

30/x-(-1x+40)=0

We get rid of parentheses

30/x+1x-40=0

We multiply all the terms by the denominator


1x*x-40*x+30=0

We add all the numbers together, and all the variables

-40x+1x*x+30=0

Wy multiply elements

x^2-40x+30=0

a = 1; b = -40; c = +30;
Δ = b2-4ac
Δ = -402-4·1·30
Δ = 1480
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:

$\sqrt{\Delta}=\sqrt{1480}=\sqrt{4*370}=\sqrt{4}*\sqrt{370}=2\sqrt{370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{370}}{2*1}=\frac{40-2\sqrt{370}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{370}}{2*1}=\frac{40+2\sqrt{370}}{2}
$