30/x-30/2x=3

Solution for 30/x-30/2x=3 equation:

30/x-30/2x=3

We move all terms to the left:

30/x-30/2x-(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


60x/2x^2+(-30x)/2x^2-3=0

We multiply all the terms by the denominator


60x+(-30x)-3*2x^2=0

Wy multiply elements

-6x^2+60x+(-30x)=0

We get rid of parentheses

-6x^2+60x-30x=0

We add all the numbers together, and all the variables

-6x^2+30x=0

a = -6; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-6)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-6}=\frac{0}{-12}
=0
$