2/5x-4/6x+30=54

Solution for 2/5x-4/6x+30=54 equation:

2/5x-4/6x+30=54

We move all terms to the left:

2/5x-4/6x+30-(54)=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 add all the numbers together, and all the variables

2/5x-4/6x-24=0

We calculate fractions


12x/30x^2+(-20x)/30x^2-24=0

We multiply all the terms by the denominator


12x+(-20x)-24*30x^2=0

Wy multiply elements

-720x^2+12x+(-20x)=0

We get rid of parentheses

-720x^2+12x-20x=0

We add all the numbers together, and all the variables

-720x^2-8x=0

a = -720; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-720)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-720}=\frac{0}{-1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-720}=\frac{16}{-1440}
=-1/90
$