2x=20/x-3

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

2x=20/x-3

We move all terms to the left:

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


Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

2x-20/x+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x+2x*x-20=0

Wy multiply elements

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