(7+x)(4+x)=256

Solution for (7+x)(4+x)=256 equation:

(7+x)(4+x)=256

We move all terms to the left:

(7+x)(4+x)-(256)=0

We add all the numbers together, and all the variables

(x+7)(x+4)-256=0

We multiply parentheses ..

(+x^2+4x+7x+28)-256=0

We get rid of parentheses

x^2+4x+7x+28-256=0

We add all the numbers together, and all the variables

x^2+11x-228=0

a = 1; b = 11; c = -228;
Δ = b2-4ac
Δ = 112-4·1·(-228)
Δ = 1033
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{-(11)-\sqrt{1033}}{2*1}=\frac{-11-\sqrt{1033}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{1033}}{2*1}=\frac{-11+\sqrt{1033}}{2}
$