20-x=35/2x

Solution for 20-x=35/2x equation:

20-x=35/2x

We move all terms to the left:

20-x-(35/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+35/2x)+20=0

We add all the numbers together, and all the variables

-1x-(+35/2x)+20=0

We get rid of parentheses

-1x-35/2x+20=0

We multiply all the terms by the denominator


-1x*2x+20*2x-35=0

Wy multiply elements

-2x^2+40x-35=0

a = -2; b = 40; c = -35;
Δ = b2-4ac
Δ = 402-4·(-2)·(-35)
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{330}}{2*-2}=\frac{-40-2\sqrt{330}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{330}}{2*-2}=\frac{-40+2\sqrt{330}}{-4}
$