(22+x)(28+x)=722

Solution for (22+x)(28+x)=722 equation:

(22+x)(28+x)=722

We move all terms to the left:

(22+x)(28+x)-(722)=0

We add all the numbers together, and all the variables

(x+22)(x+28)-722=0

We multiply parentheses ..

(+x^2+28x+22x+616)-722=0

We get rid of parentheses

x^2+28x+22x+616-722=0

We add all the numbers together, and all the variables

x^2+50x-106=0

a = 1; b = 50; c = -106;
Δ = b2-4ac
Δ = 502-4·1·(-106)
Δ = 2924
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:

$\sqrt{\Delta}=\sqrt{2924}=\sqrt{4*731}=\sqrt{4}*\sqrt{731}=2\sqrt{731}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{731}}{2*1}=\frac{-50-2\sqrt{731}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{731}}{2*1}=\frac{-50+2\sqrt{731}}{2}
$