X+(3x/x-10)=2

Solution for X+(3x/x-10)=2 equation:

X+(3X/X-10)=2

We move all terms to the left:

X+(3X/X-10)-(2)=0


Domain of the equation: X-10)!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-9X+X*X=0

Wy multiply elements

X^2-9X=0

a = 1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1}=\frac{18}{2}
=9
$