3/2x-x=40

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

3/2x-x=40

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/2x-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 = 6424
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:

$\sqrt{\Delta}=\sqrt{6424}=\sqrt{4*1606}=\sqrt{4}*\sqrt{1606}=2\sqrt{1606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1606}}{2*-2}=\frac{80-2\sqrt{1606}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1606}}{2*-2}=\frac{80+2\sqrt{1606}}{-4}
$