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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-192x^2)/216x^2+180x/216x^2+(-162x)/216x^2-2=0

We multiply all the terms by the denominator


(-192x^2)+180x+(-162x)-2*216x^2=0

Wy multiply elements

(-192x^2)-432x^2+180x+(-162x)=0

We get rid of parentheses

-192x^2-432x^2+180x-162x=0

We add all the numbers together, and all the variables

-624x^2+18x=0

a = -624; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-624)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-624}=\frac{-36}{-1248}
=3/104
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-624}=\frac{0}{-1248}
=0
$