60/x-60/2x=3

Solution for 60/x-60/2x=3 equation:

60/x-60/2x=3

We move all terms to the left:

60/x-60/2x-(3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


120x/2x^2+(-60x)/2x^2-3=0

We multiply all the terms by the denominator


120x+(-60x)-3*2x^2=0

Wy multiply elements

-6x^2+120x+(-60x)=0

We get rid of parentheses

-6x^2+120x-60x=0

We add all the numbers together, and all the variables

-6x^2+60x=0

a = -6; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-6)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-6}=\frac{-120}{-12}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-6}=\frac{0}{-12}
=0
$