(5+x)*(7+x)=99

Solution for (5+x)*(7+x)=99 equation:

(5+x)(7+x)=99

We move all terms to the left:

(5+x)(7+x)-(99)=0

We add all the numbers together, and all the variables

(x+5)(x+7)-99=0

We multiply parentheses ..

(+x^2+7x+5x+35)-99=0

We get rid of parentheses

x^2+7x+5x+35-99=0

We add all the numbers together, and all the variables

x^2+12x-64=0

a = 1; b = 12; c = -64;
Δ = b2-4ac
Δ = 122-4·1·(-64)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20}{2*1}=\frac{8}{2}
=4
$