10/2x-1=14/x+4

Solution for 10/2x-1=14/x+4 equation:

10/2x-1=14/x+4

We move all terms to the left:

10/2x-1-(14/x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

10/2x-14/x-4-1=0

We calculate fractions


10x/2x^2+(-28x)/2x^2-4-1=0

We add all the numbers together, and all the variables

10x/2x^2+(-28x)/2x^2-5=0

We multiply all the terms by the denominator


10x+(-28x)-5*2x^2=0

Wy multiply elements

-10x^2+10x+(-28x)=0

We get rid of parentheses

-10x^2+10x-28x=0

We add all the numbers together, and all the variables

-10x^2-18x=0

a = -10; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-10)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-10}=\frac{36}{-20}
=-1+4/5
$