(8/3)x+(x-6)/3=2

Solution for (8/3)x+(x-6)/3=2 equation:

(8/3)x+(x-6)/3=2

We move all terms to the left:

(8/3)x+(x-6)/3-(2)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/3)x+(x-6)/3-2=0

We multiply parentheses

8x^2+(x-6)/3-2=0

We multiply all the terms by the denominator


8x^2*3+(x-6)-2*3=0

We add all the numbers together, and all the variables

8x^2*3+(x-6)-6=0

Wy multiply elements

24x^2+(x-6)-6=0

We get rid of parentheses

24x^2+x-6-6=0

We add all the numbers together, and all the variables

24x^2+x-12=0

a = 24; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·24·(-12)
Δ = 1153
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{-(1)-\sqrt{1153}}{2*24}=\frac{-1-\sqrt{1153}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1153}}{2*24}=\frac{-1+\sqrt{1153}}{48}
$