2(3g+2)=(1/2)*(12g+8)

Solution for 2(3g+2)=(1/2)*(12g+8) equation:

2(3g+2)=(1/2)(12g+8)

We move all terms to the left:

2(3g+2)-((1/2)(12g+8))=0


Domain of the equation: 2)(12g+8))!=0

g∈R


We add all the numbers together, and all the variables

2(3g+2)-((+1/2)(12g+8))=0

We multiply parentheses

6g-((+1/2)(12g+8))+4=0

We multiply parentheses ..

-((+12g^2+1/2*8))+6g+4=0

We multiply all the terms by the denominator


-((+12g^2+1+6g*2*8))+4*2*8))=0


We calculate terms in parentheses: -((+12g^2+1+6g*2*8)), so:

(+12g^2+1+6g*2*8)

We get rid of parentheses

12g^2+6g*2*8+1

Wy multiply elements

12g^2+96g*8+1

Wy multiply elements

12g^2+768g+1

Back to the equation:

-(12g^2+768g+1)


We add all the numbers together, and all the variables

-(12g^2+768g+1)=0

We get rid of parentheses

-12g^2-768g-1=0

a = -12; b = -768; c = -1;
Δ = b2-4ac
Δ = -7682-4·(-12)·(-1)
Δ = 589776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{589776}=\sqrt{16*36861}=\sqrt{16}*\sqrt{36861}=4\sqrt{36861}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-768)-4\sqrt{36861}}{2*-12}=\frac{768-4\sqrt{36861}}{-24}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-768)+4\sqrt{36861}}{2*-12}=\frac{768+4\sqrt{36861}}{-24}
$