2x-10/x+5=x-2

Solution for 2x-10/x+5=x-2 equation:

2x-10/x+5=x-2

We move all terms to the left:

2x-10/x+5-(x-2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2x-10/x-x+2+5=0

We multiply all the terms by the denominator


2x*x-x*x+2*x+5*x-10=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

x^2+7x-10=0

a = 1; b = 7; c = -10;
Δ = b2-4ac
Δ = 72-4·1·(-10)
Δ = 89
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{-(7)-\sqrt{89}}{2*1}=\frac{-7-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{89}}{2*1}=\frac{-7+\sqrt{89}}{2}
$