(2/3)(x+12)=3x-6

Solution for (2/3)(x+12)=3x-6 equation:

(2/3)(x+12)=3x-6

We move all terms to the left:

(2/3)(x+12)-(3x-6)=0


Domain of the equation: 3)(x+12)!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)(x+12)-(3x-6)=0

We get rid of parentheses

(+2/3)(x+12)-3x+6=0

We multiply parentheses ..

(+2x^2+2/3*12)-3x+6=0

We multiply all the terms by the denominator


(+2x^2+2-3x*3*12)+6*3*12)=0

We add all the numbers together, and all the variables

(+2x^2+2-3x*3*12)=0

We get rid of parentheses

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

Wy multiply elements

2x^2-108x*1+2=0

Wy multiply elements

2x^2-108x+2=0

a = 2; b = -108; c = +2;
Δ = b2-4ac
Δ = -1082-4·2·2
Δ = 11648
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:

$\sqrt{\Delta}=\sqrt{11648}=\sqrt{64*182}=\sqrt{64}*\sqrt{182}=8\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-8\sqrt{182}}{2*2}=\frac{108-8\sqrt{182}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+8\sqrt{182}}{2*2}=\frac{108+8\sqrt{182}}{4}
$