(1/3)(6x+12)-2(x-7)=19

Solution for (1/3)(6x+12)-2(x-7)=19 equation:

(1/3)(6x+12)-2(x-7)=19

We move all terms to the left:

(1/3)(6x+12)-2(x-7)-(19)=0


Domain of the equation: 3)(6x+12)!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)(6x+12)-2(x-7)-19=0

We multiply parentheses

(+1/3)(6x+12)-2x+14-19=0

We multiply parentheses ..

(+6x^2+1/3*12)-2x+14-19=0

We multiply all the terms by the denominator


(+6x^2+1-2x*3*12)+14*3*12)-19*3*12)=0

We add all the numbers together, and all the variables

(+6x^2+1-2x*3*12)=0

We get rid of parentheses

6x^2-2x*3*12+1=0

Wy multiply elements

6x^2-72x*1+1=0

Wy multiply elements

6x^2-72x+1=0

a = 6; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·6·1
Δ = 5160
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:

$\sqrt{\Delta}=\sqrt{5160}=\sqrt{4*1290}=\sqrt{4}*\sqrt{1290}=2\sqrt{1290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1290}}{2*6}=\frac{72-2\sqrt{1290}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1290}}{2*6}=\frac{72+2\sqrt{1290}}{12}
$