4x-5=(25/x-5)

Solution for 4x-5=(25/x-5) equation:

4x-5=(25/x-5)

We move all terms to the left:

4x-5-((25/x-5))=0


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

x∈R


We multiply all the terms by the denominator


4x*x-5*x-5))-((25-5))=0

We add all the numbers together, and all the variables

4x*x-5*x-5))-(20)=0

We add all the numbers together, and all the variables

-5x+4x*x=0

Wy multiply elements

4x^2-5x=0

a = 4; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·4·0
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*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*4}=\frac{10}{8}
=1+1/4
$