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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-240x^2)/432x^2+288x/432x^2+324x/432x^2-2=0

We multiply all the terms by the denominator


(-240x^2)+288x+324x-2*432x^2=0

We add all the numbers together, and all the variables

(-240x^2)+612x-2*432x^2=0

Wy multiply elements

(-240x^2)-864x^2+612x=0

We get rid of parentheses

-240x^2-864x^2+612x=0

We add all the numbers together, and all the variables

-1104x^2+612x=0

a = -1104; b = 612; c = 0;
Δ = b2-4ac
Δ = 6122-4·(-1104)·0
Δ = 374544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{374544}=612$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(612)-612}{2*-1104}=\frac{-1224}{-2208}
=51/92
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(612)+612}{2*-1104}=\frac{0}{-2208}
=0
$