2x/x-4+2x-5/x-3=24/3

Solution for 2x/x-4+2x-5/x-3=24/3 equation:

2x/x-4+2x-5/x-3=24/3

We move all terms to the left:

2x/x-4+2x-5/x-3-(24/3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x/x+2x-5/x-4-3-8=0

We add all the numbers together, and all the variables

2x+2x/x-5/x-15=0

We multiply all the terms by the denominator


2x*x+2x-15*x-5=0

We add all the numbers together, and all the variables

-13x+2x*x-5=0

Wy multiply elements

2x^2-13x-5=0

a = 2; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·2·(-5)
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{209}}{2*2}=\frac{13-\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{209}}{2*2}=\frac{13+\sqrt{209}}{4}
$