7/2x-8)=3/(x-6)

Solution for 7/2x-8)=3/(x-6) equation:

7/2x-8)=3/(x-6)

We move all terms to the left:

7/2x-8)-(3/(x-6))=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We calculate fractions


7x/(-10x^2)-(3*2x)/(-10x^2)+(-8)=0

We add all the numbers together, and all the variables

7x/(-10x^2)-(+3*2x)/(-10x^2)+(-8)=0

We add all the numbers together, and all the variables

7x/(-10x^2)-(+3*2x)/(-10x^2)-8=0

We multiply all the terms by the denominator


-8*(-10x^2)+7x-(+3*2x)=0

We multiply parentheses

80x^2+7x-(+3*2x)=0

We get rid of parentheses

80x^2+7x-3*2x=0

Wy multiply elements

80x^2+7x-6x=0

We add all the numbers together, and all the variables

80x^2+x=0

a = 80; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·80·0
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*80}=\frac{-2}{160}
=-1/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*80}=\frac{0}{160}
=0
$