(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!=0/1

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

30/x+30/2x-3=0

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

We add all the numbers together, and all the variables

90x-3*2x^2=0

Wy multiply elements

-6x^2+90x=0

a = -6; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-6)·0
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{-(90)-90}{2*-6}=\frac{-180}{-12}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-6}=\frac{0}{-12}
=0
$