5/2x-4=10/x+3

Solution for 5/2x-4=10/x+3 equation:

5/2x-4=10/x+3

We move all terms to the left:

5/2x-4-(10/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-10/x-3-4=0

We calculate fractions


5x/2x^2+(-20x)/2x^2-3-4=0

We add all the numbers together, and all the variables

5x/2x^2+(-20x)/2x^2-7=0

We multiply all the terms by the denominator


5x+(-20x)-7*2x^2=0

Wy multiply elements

-14x^2+5x+(-20x)=0

We get rid of parentheses

-14x^2+5x-20x=0

We add all the numbers together, and all the variables

-14x^2-15x=0

a = -14; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-14)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-14}=\frac{30}{-28}
=-1+1/14
$