3/4x-1/2=5/6x+2

Solution for 3/4x-1/2=5/6x+2 equation:

3/4x-1/2=5/6x+2

We move all terms to the left:

3/4x-1/2-(5/6x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+2)!=0

x∈R


We get rid of parentheses

3/4x-5/6x-2-1/2=0

We calculate fractions


(-144x^2)/96x^2+72x/96x^2+(-80x)/96x^2-2=0

We multiply all the terms by the denominator


(-144x^2)+72x+(-80x)-2*96x^2=0

Wy multiply elements

(-144x^2)-192x^2+72x+(-80x)=0

We get rid of parentheses

-144x^2-192x^2+72x-80x=0

We add all the numbers together, and all the variables

-336x^2-8x=0

a = -336; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-336)·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*-336}=\frac{0}{-672}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-336}=\frac{16}{-672}
=-1/42
$