75/(x-2)=75/x+10

Solution for 75/(x-2)=75/x+10 equation:

75/(x-2)=75/x+10

We move all terms to the left:

75/(x-2)-(75/x+10)=0


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

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

x!=2

x∈R



Domain of the equation: x+10)!=0

x∈R


We get rid of parentheses

75/(x-2)-75/x-10=0

We calculate fractions


75x/(x^2-2x)+(-75x+150)/(x^2-2x)-10=0

We multiply all the terms by the denominator


75x+(-75x+150)-10*(x^2-2x)=0

We multiply parentheses

-10x^2+75x+(-75x+150)+20x=0

We get rid of parentheses

-10x^2+75x-75x+20x+150=0

We add all the numbers together, and all the variables

-10x^2+20x+150=0

a = -10; b = 20; c = +150;
Δ = b2-4ac
Δ = 202-4·(-10)·150
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-80}{2*-10}=\frac{-100}{-20}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+80}{2*-10}=\frac{60}{-20}
=-3
$