6/x-5+6/5x-25=2

Solution for 6/x-5+6/5x-25=2 equation:

6/x-5+6/5x-25=2

We move all terms to the left:

6/x-5+6/5x-25-(2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

6/x+6/5x-32=0

We calculate fractions


30x/5x^2+6x/5x^2-32=0

We multiply all the terms by the denominator


30x+6x-32*5x^2=0

We add all the numbers together, and all the variables

36x-32*5x^2=0

Wy multiply elements

-160x^2+36x=0

a = -160; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-160)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-160}=\frac{-72}{-320}
=9/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-160}=\frac{0}{-320}
=0
$