1/5x-4/6x=24

Solution for 1/5x-4/6x=24 equation:

1/5x-4/6x=24

We move all terms to the left:

1/5x-4/6x-(24)=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


6x/30x^2+(-20x)/30x^2-24=0

We multiply all the terms by the denominator


6x+(-20x)-24*30x^2=0

Wy multiply elements

-720x^2+6x+(-20x)=0

We get rid of parentheses

-720x^2+6x-20x=0

We add all the numbers together, and all the variables

-720x^2-14x=0

a = -720; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-720)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-720}=\frac{0}{-1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-720}=\frac{28}{-1440}
=-7/360
$