7/4x-1=2/x+4

Solution for 7/4x-1=2/x+4 equation:

7/4x-1=2/x+4

We move all terms to the left:

7/4x-1-(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-4-1=0

We calculate fractions


7x/4x^2+(-8x)/4x^2-4-1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20x^2+7x+(-8x)=0

We get rid of parentheses

-20x^2+7x-8x=0

We add all the numbers together, and all the variables

-20x^2-1x=0

a = -20; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-20)·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*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-20}=\frac{2}{-40}
=-1/20
$