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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+7x+8=0

a = 1; b = 7; c = +8;
Δ = b2-4ac
Δ = 72-4·1·8
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{17}}{2*1}=\frac{-7-\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*1}=\frac{-7+\sqrt{17}}{2}
$