3/2x=40-x

Solution for 3/2x=40-x equation:

3/2x=40-x

We move all terms to the left:

3/2x-(40-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(-1x+40)=0

We get rid of parentheses

3/2x+1x-40=0

We multiply all the terms by the denominator


1x*2x-40*2x+3=0

Wy multiply elements

2x^2-80x+3=0

a = 2; b = -80; c = +3;
Δ = b2-4ac
Δ = -802-4·2·3
Δ = 6376
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:

$\sqrt{\Delta}=\sqrt{6376}=\sqrt{4*1594}=\sqrt{4}*\sqrt{1594}=2\sqrt{1594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1594}}{2*2}=\frac{80-2\sqrt{1594}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1594}}{2*2}=\frac{80+2\sqrt{1594}}{4}
$