(X+2)x+3)=x2+5x+6

Solution for (X+2)x+3)=x2+5x+6 equation:

(X+2)X+3)=X2+5X+6

We move all terms to the left:

(X+2)X+3)-(X2+5X+6)=0

We add all the numbers together, and all the variables

X^2+(X+2)X+5X+3)-(+6)=0

We add all the numbers together, and all the variables

X^2+5X+(X+2)X=0

We multiply parentheses

X^2+X^2+5X+2X=0

We add all the numbers together, and all the variables

2X^2+7X=0

a = 2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*2}=\frac{-14}{4}
=-3+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*2}=\frac{0}{4}
=0
$