4/3x-25=1/x-5

Solution for 4/3x-25=1/x-5 equation:

4/3x-25=1/x-5

We move all terms to the left:

4/3x-25-(1/x-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/3x-1/x+5-25=0

We calculate fractions


4x/3x^2+(-3x)/3x^2+5-25=0

We add all the numbers together, and all the variables

4x/3x^2+(-3x)/3x^2-20=0

We multiply all the terms by the denominator


4x+(-3x)-20*3x^2=0

Wy multiply elements

-60x^2+4x+(-3x)=0

We get rid of parentheses

-60x^2+4x-3x=0

We add all the numbers together, and all the variables

-60x^2+x=0

a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·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*-60}=\frac{-2}{-120}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-60}=\frac{0}{-120}
=0
$