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

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

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

We move all terms to the left:

4/4x-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

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-180x^2-432x^2+432x-288x=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{-288}{-1224}
=4/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-612}=\frac{0}{-1224}
=0
$