(21+x)(22+x)=26

Solution for (21+x)(22+x)=26 equation:

(21+x)(22+x)=26

We move all terms to the left:

(21+x)(22+x)-(26)=0

We add all the numbers together, and all the variables

(x+21)(x+22)-26=0

We multiply parentheses ..

(+x^2+22x+21x+462)-26=0

We get rid of parentheses

x^2+22x+21x+462-26=0

We add all the numbers together, and all the variables

x^2+43x+436=0

a = 1; b = 43; c = +436;
Δ = b2-4ac
Δ = 432-4·1·436
Δ = 105
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{-(43)-\sqrt{105}}{2*1}=\frac{-43-\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{105}}{2*1}=\frac{-43+\sqrt{105}}{2}
$