40-1/2x=x

Solution for 40-1/2x=x equation:

40-1/2x=x

We move all terms to the left:

40-1/2x-(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

-1x-1/2x+40=0

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2+80x-1=0

a = -2; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·(-2)·(-1)
Δ = 6392
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:

$\sqrt{\Delta}=\sqrt{6392}=\sqrt{4*1598}=\sqrt{4}*\sqrt{1598}=2\sqrt{1598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1598}}{2*-2}=\frac{-80-2\sqrt{1598}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1598}}{2*-2}=\frac{-80+2\sqrt{1598}}{-4}
$