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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(5(X+3)), so:

5(X+3)

We multiply parentheses

5X+15

Back to the equation:

-(5X+15)


We get rid of parentheses

X^2+3X+2X-5X+6-15=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
$