5/x-3+6/2x-6=4

Solution for 5/x-3+6/2x-6=4 equation:

5/x-3+6/2x-6=4

We move all terms to the left:

5/x-3+6/2x-6-(4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/x+6/2x-13=0

We calculate fractions


10x/2x^2+6x/2x^2-13=0

We multiply all the terms by the denominator


10x+6x-13*2x^2=0

We add all the numbers together, and all the variables

16x-13*2x^2=0

Wy multiply elements

-26x^2+16x=0

a = -26; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-26)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-26}=\frac{-32}{-52}
=8/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-26}=\frac{0}{-52}
=0
$