(1/5x)-(1/4x)=-17/60

Solution for (1/5x)-(1/4x)=-17/60 equation:

(1/5x)-(1/4x)=-17/60

We move all terms to the left:

(1/5x)-(1/4x)-(-17/60)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/5x)-(+1/4x)-(-17/60)=0

We get rid of parentheses

1/5x-1/4x+17/60=0

We calculate fractions


1360x^2/7200x^2+1440x/7200x^2+(-1800x)/7200x^2=0

We multiply all the terms by the denominator


1360x^2+1440x+(-1800x)=0

We get rid of parentheses

1360x^2+1440x-1800x=0

We add all the numbers together, and all the variables

1360x^2-360x=0

a = 1360; b = -360; c = 0;
Δ = b2-4ac
Δ = -3602-4·1360·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-360}{2*1360}=\frac{0}{2720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+360}{2*1360}=\frac{720}{2720}
=9/34
$