(x+5)(x+1)=7

Solution for (x+5)(x+1)=7 equation:

(x+5)(x+1)=7

We move all terms to the left:

(x+5)(x+1)-(7)=0

We multiply parentheses ..

(+x^2+x+5x+5)-7=0

We get rid of parentheses

x^2+x+5x+5-7=0

We add all the numbers together, and all the variables

x^2+6x-2=0

a = 1; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·1·(-2)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*1}=\frac{-6-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*1}=\frac{-6+2\sqrt{11}}{2}
$