(5/6x)-(1/5x)=19

Solution for (5/6x)-(1/5x)=19 equation:

(5/6x)-(1/5x)=19

We move all terms to the left:

(5/6x)-(1/5x)-(19)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6x)-(+1/5x)-19=0

We get rid of parentheses

5/6x-1/5x-19=0

We calculate fractions


25x/30x^2+(-6x)/30x^2-19=0

We multiply all the terms by the denominator


25x+(-6x)-19*30x^2=0

Wy multiply elements

-570x^2+25x+(-6x)=0

We get rid of parentheses

-570x^2+25x-6x=0

We add all the numbers together, and all the variables

-570x^2+19x=0

a = -570; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-570)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-570}=\frac{-38}{-1140}
=1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-570}=\frac{0}{-1140}
=0
$