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 get rid of parentheses

7/2x-3/x+6-8=0

We calculate fractions


7x/2x^2+(-6x)/2x^2+6-8=0

We add all the numbers together, and all the variables

7x/2x^2+(-6x)/2x^2-2=0

We multiply all the terms by the denominator


7x+(-6x)-2*2x^2=0

Wy multiply elements

-4x^2+7x+(-6x)=0

We get rid of parentheses

-4x^2+7x-6x=0

We add all the numbers together, and all the variables

-4x^2+x=0

a = -4; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-4)·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*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-4}=\frac{0}{-8}
=0
$