7/4x+4=3/x-5

Solution for 7/4x+4=3/x-5 equation:

7/4x+4=3/x-5

We move all terms to the left:

7/4x+4-(3/x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

7/4x-3/x+5+4=0

We calculate fractions


7x/4x^2+(-12x)/4x^2+5+4=0

We add all the numbers together, and all the variables

7x/4x^2+(-12x)/4x^2+9=0

We multiply all the terms by the denominator


7x+(-12x)+9*4x^2=0

Wy multiply elements

36x^2+7x+(-12x)=0

We get rid of parentheses

36x^2+7x-12x=0

We add all the numbers together, and all the variables

36x^2-5x=0

a = 36; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·36·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*36}=\frac{10}{72}
=5/36
$