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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-180x^2)/432x^2+324x/432x^2+(-288x)/432x^2-1=0

We multiply all the terms by the denominator


(-180x^2)+324x+(-288x)-1*432x^2=0

Wy multiply elements

(-180x^2)-432x^2+324x+(-288x)=0

We get rid of parentheses

-180x^2-432x^2+324x-288x=0

We add all the numbers together, and all the variables

-612x^2+36x=0

a = -612; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-612)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-612}=\frac{-72}{-1224}
=1/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-612}=\frac{0}{-1224}
=0
$