1/5x-30-1=8/x-6

Solution for 1/5x-30-1=8/x-6 equation:

1/5x-30-1=8/x-6

We move all terms to the left:

1/5x-30-1-(8/x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x-6)!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(8/x-6)-31=0

We get rid of parentheses

1/5x-8/x+6-31=0

We calculate fractions


x/5x^2+(-40x)/5x^2+6-31=0

We add all the numbers together, and all the variables

x/5x^2+(-40x)/5x^2-25=0

We multiply all the terms by the denominator


x+(-40x)-25*5x^2=0

Wy multiply elements

-125x^2+x+(-40x)=0

We get rid of parentheses

-125x^2+x-40x=0

We add all the numbers together, and all the variables

-125x^2-39x=0

a = -125; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·(-125)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*-125}=\frac{0}{-250}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*-125}=\frac{78}{-250}
=-39/125
$