2/3x+2=12x-48+2

Solution for 2/3x+2=12x-48+2 equation:

2/3x+2=12x-48+2

We move all terms to the left:

2/3x+2-(12x-48+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(12x-46)+2=0

We get rid of parentheses

2/3x-12x+46+2=0

We multiply all the terms by the denominator


-12x*3x+46*3x+2*3x+2=0

Wy multiply elements

-36x^2+138x+6x+2=0

We add all the numbers together, and all the variables

-36x^2+144x+2=0

a = -36; b = 144; c = +2;
Δ = b2-4ac
Δ = 1442-4·(-36)·2
Δ = 21024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{21024}=\sqrt{144*146}=\sqrt{144}*\sqrt{146}=12\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-12\sqrt{146}}{2*-36}=\frac{-144-12\sqrt{146}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+12\sqrt{146}}{2*-36}=\frac{-144+12\sqrt{146}}{-72}
$