2/5x+6=3/x-4

Solution for 2/5x+6=3/x-4 equation:

2/5x+6=3/x-4

We move all terms to the left:

2/5x+6-(3/x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

2/5x-3/x+4+6=0

We calculate fractions


2x/5x^2+(-15x)/5x^2+4+6=0

We add all the numbers together, and all the variables

2x/5x^2+(-15x)/5x^2+10=0

We multiply all the terms by the denominator


2x+(-15x)+10*5x^2=0

Wy multiply elements

50x^2+2x+(-15x)=0

We get rid of parentheses

50x^2+2x-15x=0

We add all the numbers together, and all the variables

50x^2-13x=0

a = 50; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·50·0
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*50}=\frac{0}{100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*50}=\frac{26}{100}
=13/50
$