3/5x-1/6x=38

Solution for 3/5x-1/6x=38 equation:

3/5x-1/6x=38

We move all terms to the left:

3/5x-1/6x-(38)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


18x/30x^2+(-5x)/30x^2-38=0

We multiply all the terms by the denominator


18x+(-5x)-38*30x^2=0

Wy multiply elements

-1140x^2+18x+(-5x)=0

We get rid of parentheses

-1140x^2+18x-5x=0

We add all the numbers together, and all the variables

-1140x^2+13x=0

a = -1140; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-1140)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-1140}=\frac{-26}{-2280}
=13/1140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1140}=\frac{0}{-2280}
=0
$