2x/x-4+2x-5/x-3=81/3

Solution for 2x/x-4+2x-5/x-3=81/3 equation:

2x/x-4+2x-5/x-3=81/3

We move all terms to the left:

2x/x-4+2x-5/x-3-(81/3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x/x+2x-5/x-4-3-27=0

We add all the numbers together, and all the variables

2x+2x/x-5/x-34=0

We multiply all the terms by the denominator


2x*x+2x-34*x-5=0

We add all the numbers together, and all the variables

-32x+2x*x-5=0

Wy multiply elements

2x^2-32x-5=0

a = 2; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·2·(-5)
Δ = 1064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{266}}{2*2}=\frac{32-2\sqrt{266}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{266}}{2*2}=\frac{32+2\sqrt{266}}{4}
$