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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


48x^2/432x^2+288x/432x^2+324x/432x^2-4=0

We multiply all the terms by the denominator


48x^2+288x+324x-4*432x^2=0

We add all the numbers together, and all the variables

48x^2+612x-4*432x^2=0

Wy multiply elements

48x^2-1728x^2+612x=0

We add all the numbers together, and all the variables

-1680x^2+612x=0

a = -1680; b = 612; c = 0;
Δ = b2-4ac
Δ = 6122-4·(-1680)·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*-1680}=\frac{-1224}{-3360}
=51/140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(612)+612}{2*-1680}=\frac{0}{-3360}
=0
$