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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-324x^2)/288x^2+96x/288x^2+(-240x)/288x^2-3=0

We multiply all the terms by the denominator


(-324x^2)+96x+(-240x)-3*288x^2=0

Wy multiply elements

(-324x^2)-864x^2+96x+(-240x)=0

We get rid of parentheses

-324x^2-864x^2+96x-240x=0

We add all the numbers together, and all the variables

-1188x^2-144x=0

a = -1188; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-1188)·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*-1188}=\frac{0}{-2376}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-1188}=\frac{288}{-2376}
=-4/33
$