(1)/(3x)+(5)/(6x)=(3)/(5)

Solution for (1)/(3x)+(5)/(6x)=(3)/(5) equation:

(1)/(3x)+(5)/(6x)=(3)/(5)

We move all terms to the left:

(1)/(3x)+(5)/(6x)-((3)/(5))=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x+5/6x-(+3/5)=0

We get rid of parentheses

1/3x+5/6x-3/5=0

We calculate fractions


(-324x^2)/450x^2+150x/450x^2+375x/450x^2=0

We multiply all the terms by the denominator


(-324x^2)+150x+375x=0

We add all the numbers together, and all the variables

(-324x^2)+525x=0

We get rid of parentheses

-324x^2+525x=0

a = -324; b = 525; c = 0;
Δ = b2-4ac
Δ = 5252-4·(-324)·0
Δ = 275625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{275625}=525$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(525)-525}{2*-324}=\frac{-1050}{-648}
=1+67/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(525)+525}{2*-324}=\frac{0}{-648}
=0
$