2/3x+1=2x+2

Solution for 2/3x+1=2x+2 equation:

2/3x+1=2x+2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*3x-2*3x+1*3x+2=0

Wy multiply elements

-6x^2-6x+3x+2=0

We add all the numbers together, and all the variables

-6x^2-3x+2=0

a = -6; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-6)·2
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{57}}{2*-6}=\frac{3-\sqrt{57}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*-6}=\frac{3+\sqrt{57}}{-12}
$