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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


324x^2/288x^2+96x/288x^2+(-240x)/288x^2+1=0

We multiply all the terms by the denominator


324x^2+96x+(-240x)+1*288x^2=0

Wy multiply elements

324x^2+288x^2+96x+(-240x)=0

We get rid of parentheses

324x^2+288x^2+96x-240x=0

We add all the numbers together, and all the variables

612x^2-144x=0

a = 612; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·612·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*612}=\frac{0}{1224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*612}=\frac{288}{1224}
=4/17
$