52/4x-25=32/x+8

Solution for 52/4x-25=32/x+8 equation:

52/4x-25=32/x+8

We move all terms to the left:

52/4x-25-(32/x+8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x+8)!=0

x∈R


We get rid of parentheses

52/4x-32/x-8-25=0

We calculate fractions


52x/4x^2+(-128x)/4x^2-8-25=0

We add all the numbers together, and all the variables

52x/4x^2+(-128x)/4x^2-33=0

We multiply all the terms by the denominator


52x+(-128x)-33*4x^2=0

Wy multiply elements

-132x^2+52x+(-128x)=0

We get rid of parentheses

-132x^2+52x-128x=0

We add all the numbers together, and all the variables

-132x^2-76x=0

a = -132; b = -76; c = 0;
Δ = b2-4ac
Δ = -762-4·(-132)·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-76}{2*-132}=\frac{0}{-264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+76}{2*-132}=\frac{152}{-264}
=-19/33
$