x(x+3)=3(x+2)+3

Solution for x(x+3)=3(x+2)+3 equation:

x(x+3)=3(x+2)+3

We move all terms to the left:

x(x+3)-(3(x+2)+3)=0

We multiply parentheses

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


We calculate terms in parentheses: -(3(x+2)+3), so:

3(x+2)+3

We multiply parentheses

3x+6+3

We add all the numbers together, and all the variables

3x+9

Back to the equation:

-(3x+9)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-9=0

a = 1; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·1·(-9)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*1}=\frac{6}{2}
=3
$