(3+x)(1+x)=22

Solution for (3+x)(1+x)=22 equation:

(3+x)(1+x)=22

We move all terms to the left:

(3+x)(1+x)-(22)=0

We add all the numbers together, and all the variables

(x+3)(x+1)-22=0

We multiply parentheses ..

(+x^2+x+3x+3)-22=0

We get rid of parentheses

x^2+x+3x+3-22=0

We add all the numbers together, and all the variables

x^2+4x-19=0

a = 1; b = 4; c = -19;
Δ = b2-4ac
Δ = 42-4·1·(-19)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{23}}{2*1}=\frac{-4-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{23}}{2*1}=\frac{-4+2\sqrt{23}}{2}
$