(7+x)(12+x)=176

Solution for (7+x)(12+x)=176 equation:

(7+x)(12+x)=176

We move all terms to the left:

(7+x)(12+x)-(176)=0

We add all the numbers together, and all the variables

(x+7)(x+12)-176=0

We multiply parentheses ..

(+x^2+12x+7x+84)-176=0

We get rid of parentheses

x^2+12x+7x+84-176=0

We add all the numbers together, and all the variables

x^2+19x-92=0

a = 1; b = 19; c = -92;
Δ = b2-4ac
Δ = 192-4·1·(-92)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-27}{2*1}=\frac{-46}{2}
=-23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+27}{2*1}=\frac{8}{2}
=4
$