3=x-10/x-2

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

3=x-10/x-2

We move all terms to the left:

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


Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

-x+10/x+2+3=0

We multiply all the terms by the denominator


-x*x+2*x+3*x+10=0

We add all the numbers together, and all the variables

5x-x*x+10=0

Wy multiply elements

-1x^2+5x+10=0

a = -1; b = 5; c = +10;
Δ = b2-4ac
Δ = 52-4·(-1)·10
Δ = 65
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{-(5)-\sqrt{65}}{2*-1}=\frac{-5-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*-1}=\frac{-5+\sqrt{65}}{-2}
$