1/12x+10=1/4x+54

Solution for 1/12x+10=1/4x+54 equation:

1/12x+10=1/4x+54

We move all terms to the left:

1/12x+10-(1/4x+54)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 4x+54)!=0

x∈R


We get rid of parentheses

1/12x-1/4x-54+10=0

We calculate fractions


4x/48x^2+(-12x)/48x^2-54+10=0

We add all the numbers together, and all the variables

4x/48x^2+(-12x)/48x^2-44=0

We multiply all the terms by the denominator


4x+(-12x)-44*48x^2=0

Wy multiply elements

-2112x^2+4x+(-12x)=0

We get rid of parentheses

-2112x^2+4x-12x=0

We add all the numbers together, and all the variables

-2112x^2-8x=0

a = -2112; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-2112)·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*-2112}=\frac{0}{-4224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-2112}=\frac{16}{-4224}
=-1/264
$