(20-3x)/x=2x

Solution for (20-3x)/x=2x equation:

(20-3x)/x=2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

a = -2; b = -3; c = +20;
Δ = b2-4ac
Δ = -32-4·(-2)·20
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*-2}=\frac{16}{-4}
=-4
$