3(4g+6)=2g(6g+9)

Solution for 3(4g+6)=2g(6g+9) equation:

3(4g+6)=2g(6g+9)

We move all terms to the left:

3(4g+6)-(2g(6g+9))=0

We multiply parentheses

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


We calculate terms in parentheses: -(2g(6g+9)), so:

2g(6g+9)

We multiply parentheses

12g^2+18g

Back to the equation:

-(12g^2+18g)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -12; b = -6; c = +18;
Δ = b2-4ac
Δ = -62-4·(-12)·18
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*-12}=\frac{-24}{-24}
=1
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-12}=\frac{36}{-24}
=-1+1/2
$