3g(4g+6)=(6g+9)

Solution for 3g(4g+6)=(6g+9) equation:

3g(4g+6)=(6g+9)

We move all terms to the left:

3g(4g+6)-((6g+9))=0

We multiply parentheses

12g^2+18g-((6g+9))=0


We calculate terms in parentheses: -((6g+9)), so:

(6g+9)

We get rid of parentheses

6g+9

Back to the equation:

-(6g+9)


We get rid of parentheses

12g^2+18g-6g-9=0

We add all the numbers together, and all the variables

12g^2+12g-9=0

a = 12; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·12·(-9)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*12}=\frac{-36}{24}
=-1+1/2
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*12}=\frac{12}{24}
=1/2
$