100=(8+x)(5+x)

Solution for 100=(8+x)(5+x) equation:

100=(8+x)(5+x)

We move all terms to the left:

100-((8+x)(5+x))=0

We add all the numbers together, and all the variables

-((x+8)(x+5))+100=0

We multiply parentheses ..

-((+x^2+5x+8x+40))+100=0


We calculate terms in parentheses: -((+x^2+5x+8x+40)), so:

(+x^2+5x+8x+40)

We get rid of parentheses

x^2+5x+8x+40

We add all the numbers together, and all the variables

x^2+13x+40

Back to the equation:

-(x^2+13x+40)


We get rid of parentheses

-x^2-13x-40+100=0

We add all the numbers together, and all the variables

-1x^2-13x+60=0

a = -1; b = -13; c = +60;
Δ = b2-4ac
Δ = -132-4·(-1)·60
Δ = 409
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{-(-13)-\sqrt{409}}{2*-1}=\frac{13-\sqrt{409}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{409}}{2*-1}=\frac{13+\sqrt{409}}{-2}
$