(x+4)(x+7)=56

Solution for (x+4)(x+7)=56 equation:

(x+4)(x+7)=56

We move all terms to the left:

(x+4)(x+7)-(56)=0

We multiply parentheses ..

(+x^2+7x+4x+28)-56=0

We get rid of parentheses

x^2+7x+4x+28-56=0

We add all the numbers together, and all the variables

x^2+11x-28=0

a = 1; b = 11; c = -28;
Δ = b2-4ac
Δ = 112-4·1·(-28)
Δ = 233
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{233}}{2*1}=\frac{-11-\sqrt{233}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{233}}{2*1}=\frac{-11+\sqrt{233}}{2}
$