20=x+3/2x

Solution for 20=x+3/2x equation:

20=x+3/2x

We move all terms to the left:

20-(x+3/2x)=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+3/2x)+20=0

We get rid of parentheses

-x-3/2x+20=0

We multiply all the terms by the denominator


-x*2x+20*2x-3=0

Wy multiply elements

-2x^2+40x-3=0

a = -2; b = 40; c = -3;
Δ = b2-4ac
Δ = 402-4·(-2)·(-3)
Δ = 1576
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:

$\sqrt{\Delta}=\sqrt{1576}=\sqrt{4*394}=\sqrt{4}*\sqrt{394}=2\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{394}}{2*-2}=\frac{-40-2\sqrt{394}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{394}}{2*-2}=\frac{-40+2\sqrt{394}}{-4}
$