8/x=20/2x+3

Solution for 8/x=20/2x+3 equation:

8/x=20/2x+3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

8/x-20/2x-3=0

We calculate fractions


16x/2x^2+(-20x)/2x^2-3=0

We multiply all the terms by the denominator


16x+(-20x)-3*2x^2=0

Wy multiply elements

-6x^2+16x+(-20x)=0

We get rid of parentheses

-6x^2+16x-20x=0

We add all the numbers together, and all the variables

-6x^2-4x=0

a = -6; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-6)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-6}=\frac{8}{-12}
=-2/3
$