2x-10/x+4+3=x-2/x-3+4

Solution for 2x-10/x+4+3=x-2/x-3+4 equation:

2x-10/x+4+3=x-2/x-3+4

We move all terms to the left:

2x-10/x+4+3-(x-2/x-3+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-3+4)!=0

We move all terms containing x to the left, all other terms to the right

x+4)!=3

x∈R


We add all the numbers together, and all the variables

2x-10/x-(x-2/x+1)+4+3=0

We add all the numbers together, and all the variables

2x-10/x-(x-2/x+1)+7=0

We get rid of parentheses

2x-10/x-x+2/x-1+7=0

We multiply all the terms by the denominator


2x*x-x*x-1*x+7*x-10+2=0

We add all the numbers together, and all the variables

6x+2x*x-x*x-8=0

Wy multiply elements

2x^2-1x^2+6x-8=0

We add all the numbers together, and all the variables

x^2+6x-8=0

a = 1; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·1·(-8)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*1}=\frac{-6-2\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*1}=\frac{-6+2\sqrt{17}}{2}
$