60/x-60/(x+15)=2

Solution for 60/x-60/(x+15)=2 equation:

60/x-60/(x+15)=2

We move all terms to the left:

60/x-60/(x+15)-(2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+15)!=0

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

x!=-15

x∈R


We calculate fractions


(60x+900)/(x^2+15x)+(-60x)/(x^2+15x)-2=0

We multiply all the terms by the denominator


(60x+900)+(-60x)-2*(x^2+15x)=0

We multiply parentheses

-2x^2+(60x+900)+(-60x)-30x=0

We get rid of parentheses

-2x^2+60x-60x-30x+900=0

We add all the numbers together, and all the variables

-2x^2-30x+900=0

a = -2; b = -30; c = +900;
Δ = b2-4ac
Δ = -302-4·(-2)·900
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-90}{2*-2}=\frac{-60}{-4}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+90}{2*-2}=\frac{120}{-4}
=-30
$