5/12x-3/4=1/6x+1

Solution for 5/12x-3/4=1/6x+1 equation:

5/12x-3/4=1/6x+1

We move all terms to the left:

5/12x-3/4-(1/6x+1)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

5/12x-1/6x-1-3/4=0

We calculate fractions


(-1296x^2)/1152x^2+480x/1152x^2+(-192x)/1152x^2-1=0

We multiply all the terms by the denominator


(-1296x^2)+480x+(-192x)-1*1152x^2=0

Wy multiply elements

(-1296x^2)-1152x^2+480x+(-192x)=0

We get rid of parentheses

-1296x^2-1152x^2+480x-192x=0

We add all the numbers together, and all the variables

-2448x^2+288x=0

a = -2448; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·(-2448)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*-2448}=\frac{-576}{-4896}
=2/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*-2448}=\frac{0}{-4896}
=0
$