(x+17)(x+5)=-2

Solution for (x+17)(x+5)=-2 equation:

(x+17)(x+5)=-2

We move all terms to the left:

(x+17)(x+5)-(-2)=0

We add all the numbers together, and all the variables

(x+17)(x+5)+2=0

We multiply parentheses ..

(+x^2+5x+17x+85)+2=0

We get rid of parentheses

x^2+5x+17x+85+2=0

We add all the numbers together, and all the variables

x^2+22x+87=0

a = 1; b = 22; c = +87;
Δ = b2-4ac
Δ = 222-4·1·87
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{34}}{2*1}=\frac{-22-2\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{34}}{2*1}=\frac{-22+2\sqrt{34}}{2}
$