(X+1)(x+3)=7

Solution for (X+1)(x+3)=7 equation:

(X+1)(X+3)=7

We move all terms to the left:

(X+1)(X+3)-(7)=0

We multiply parentheses ..

(+X^2+3X+X+3)-7=0

We get rid of parentheses

X^2+3X+X+3-7=0

We add all the numbers together, and all the variables

X^2+4X-4=0

a = 1; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·1·(-4)
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{-(4)-4\sqrt{2}}{2*1}=\frac{-4-4\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*1}=\frac{-4+4\sqrt{2}}{2}
$