(x+19)(x+22)=21

Solution for (x+19)(x+22)=21 equation:

(x+19)(x+22)=21

We move all terms to the left:

(x+19)(x+22)-(21)=0

We multiply parentheses ..

(+x^2+22x+19x+418)-21=0

We get rid of parentheses

x^2+22x+19x+418-21=0

We add all the numbers together, and all the variables

x^2+41x+397=0

a = 1; b = 41; c = +397;
Δ = b2-4ac
Δ = 412-4·1·397
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-\sqrt{93}}{2*1}=\frac{-41-\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{93}}{2*1}=\frac{-41+\sqrt{93}}{2}
$