(x+12)(x+14)=22

Solution for (x+12)(x+14)=22 equation:

(x+12)(x+14)=22

We move all terms to the left:

(x+12)(x+14)-(22)=0

We multiply parentheses ..

(+x^2+14x+12x+168)-22=0

We get rid of parentheses

x^2+14x+12x+168-22=0

We add all the numbers together, and all the variables

x^2+26x+146=0

a = 1; b = 26; c = +146;
Δ = b2-4ac
Δ = 262-4·1·146
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{-(26)-2\sqrt{23}}{2*1}=\frac{-26-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{23}}{2*1}=\frac{-26+2\sqrt{23}}{2}
$