7/4x-5=2/x+4

Solution for 7/4x-5=2/x+4 equation:

7/4x-5=2/x+4

We move all terms to the left:

7/4x-5-(2/x+4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

7/4x-2/x-4-5=0

We calculate fractions


7x/4x^2+(-8x)/4x^2-4-5=0

We add all the numbers together, and all the variables

7x/4x^2+(-8x)/4x^2-9=0

We multiply all the terms by the denominator


7x+(-8x)-9*4x^2=0

Wy multiply elements

-36x^2+7x+(-8x)=0

We get rid of parentheses

-36x^2+7x-8x=0

We add all the numbers together, and all the variables

-36x^2-1x=0

a = -36; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-36)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-36}=\frac{2}{-72}
=-1/36
$