5/2x+6=-4/x

Solution for 5/2x+6=-4/x equation:

5/2x+6=-4/x

We move all terms to the left:

5/2x+6-(-4/x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

5/2x+4/x+6=0

We calculate fractions


5x/2x^2+8x/2x^2+6=0

We multiply all the terms by the denominator


5x+8x+6*2x^2=0

We add all the numbers together, and all the variables

13x+6*2x^2=0

Wy multiply elements

12x^2+13x=0

a = 12; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·12·0
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{-(13)-13}{2*12}=\frac{-26}{24}
=-1+1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*12}=\frac{0}{24}
=0
$