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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2(6g+9)

We multiply parentheses

12g+18

Back to the equation:

-(12g+18)


We get rid of parentheses

12g^2+18g-12g-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{-36}{24}
=-1+1/2
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*12}=\frac{24}{24}
=1
$