(x+2)(x+5)=(x+9)

Solution for (x+2)(x+5)=(x+9) equation:

(x+2)(x+5)=(x+9)

We move all terms to the left:

(x+2)(x+5)-((x+9))=0

We multiply parentheses ..

(+x^2+5x+2x+10)-((x+9))=0


We calculate terms in parentheses: -((x+9)), so:

(x+9)

We get rid of parentheses

x+9

Back to the equation:

-(x+9)


We get rid of parentheses

x^2+5x+2x-x+10-9=0

We add all the numbers together, and all the variables

x^2+6x+1=0

a = 1; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·1·1
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{2}}{2*1}=\frac{-6-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{2}}{2*1}=\frac{-6+4\sqrt{2}}{2}
$