7/x-1+15/3x-1=8

Solution for 7/x-1+15/3x-1=8 equation:

7/x-1+15/3x-1=8

We move all terms to the left:

7/x-1+15/3x-1-(8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7/x+15/3x-10=0

We calculate fractions


21x/3x^2+15x/3x^2-10=0

We multiply all the terms by the denominator


21x+15x-10*3x^2=0

We add all the numbers together, and all the variables

36x-10*3x^2=0

Wy multiply elements

-30x^2+36x=0

a = -30; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-30)·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*-30}=\frac{-72}{-60}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-30}=\frac{0}{-60}
=0
$