(X+2)(9x)=(x+2)(27)

Solution for (X+2)(9x)=(x+2)(27) equation:

(X+2)(9X)=(X+2)(27)

We move all terms to the left:

(X+2)(9X)-((X+2)(27))=0

We multiply parentheses

9X^2+18X-((X+2)27)=0


We calculate terms in parentheses: -((X+2)27), so:

(X+2)27

We multiply parentheses

27X+54

Back to the equation:

-(27X+54)


We get rid of parentheses

9X^2+18X-27X-54=0

We add all the numbers together, and all the variables

9X^2-9X-54=0

a = 9; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·9·(-54)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-45}{2*9}=\frac{-36}{18}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+45}{2*9}=\frac{54}{18}
=3
$