5/2x-8=6/x+3

Solution for 5/2x-8=6/x+3 equation:

5/2x-8=6/x+3

We move all terms to the left:

5/2x-8-(6/x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/2x-6/x-3-8=0

We calculate fractions


5x/2x^2+(-12x)/2x^2-3-8=0

We add all the numbers together, and all the variables

5x/2x^2+(-12x)/2x^2-11=0

We multiply all the terms by the denominator


5x+(-12x)-11*2x^2=0

Wy multiply elements

-22x^2+5x+(-12x)=0

We get rid of parentheses

-22x^2+5x-12x=0

We add all the numbers together, and all the variables

-22x^2-7x=0

a = -22; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-22)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-22}=\frac{0}{-44}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-22}=\frac{14}{-44}
=-7/22
$