3x(3+x)=48+9x

Solution for 3x(3+x)=48+9x equation:

3x(3+x)=48+9x

We move all terms to the left:

3x(3+x)-(48+9x)=0

We add all the numbers together, and all the variables

3x(x+3)-(9x+48)=0

We multiply parentheses

3x^2+9x-(9x+48)=0

We get rid of parentheses

3x^2+9x-9x-48=0

We add all the numbers together, and all the variables

3x^2-48=0

a = 3; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·3·(-48)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*3}=\frac{24}{6}
=4
$