(X+7)(x+4)=180

Solution for (X+7)(x+4)=180 equation:

(X+7)(X+4)=180

We move all terms to the left:

(X+7)(X+4)-(180)=0

We multiply parentheses ..

(+X^2+4X+7X+28)-180=0

We get rid of parentheses

X^2+4X+7X+28-180=0

We add all the numbers together, and all the variables

X^2+11X-152=0

a = 1; b = 11; c = -152;
Δ = b2-4ac
Δ = 112-4·1·(-152)
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{-(11)-27}{2*1}=\frac{-38}{2}
=-19
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+27}{2*1}=\frac{16}{2}
=8
$