6(2/3x+2)=6(1/6x+6)

Solution for 6(2/3x+2)=6(1/6x+6) equation:

6(2/3x+2)=6(1/6x+6)

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R



Domain of the equation: 6x+6))!=0

x∈R


We multiply parentheses

12x-(6(1/6x+6))+12=0

We multiply all the terms by the denominator


12x*6x+12*6x+6))-(6(1+6))=0

We add all the numbers together, and all the variables

12x*6x+12*6x+6))-(67)=0

We add all the numbers together, and all the variables

12x*6x+12*6x=0

Wy multiply elements

72x^2+72x=0

a = 72; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·72·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*72}=\frac{-144}{144}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*72}=\frac{0}{144}
=0
$