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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+x^2+5x+2x+10)-((x+3))=0


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

(x+3)

We get rid of parentheses

x+3

Back to the equation:

-(x+3)


We get rid of parentheses

x^2+5x+2x-x+10-3=0

We add all the numbers together, and all the variables

x^2+6x+7=0

a = 1; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·1·7
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{2}}{2*1}=\frac{-6-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{2}}{2*1}=\frac{-6+2\sqrt{2}}{2}
$