4w(w+3)=9+12w

Solution for 4w(w+3)=9+12w equation:

4w(w+3)=9+12w

We move all terms to the left:

4w(w+3)-(9+12w)=0

We add all the numbers together, and all the variables

4w(w+3)-(12w+9)=0

We multiply parentheses

4w^2+12w-(12w+9)=0

We get rid of parentheses

4w^2+12w-12w-9=0

We add all the numbers together, and all the variables

4w^2-9=0

a = 4; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·4·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*4}=\frac{-12}{8}
=-1+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*4}=\frac{12}{8}
=1+1/2
$