(X+4)(x+5)=76

Solution for (X+4)(x+5)=76 equation:

(X+4)(X+5)=76

We move all terms to the left:

(X+4)(X+5)-(76)=0

We multiply parentheses ..

(+X^2+5X+4X+20)-76=0

We get rid of parentheses

X^2+5X+4X+20-76=0

We add all the numbers together, and all the variables

X^2+9X-56=0

a = 1; b = 9; c = -56;
Δ = b2-4ac
Δ = 92-4·1·(-56)
Δ = 305
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{-(9)-\sqrt{305}}{2*1}=\frac{-9-\sqrt{305}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{305}}{2*1}=\frac{-9+\sqrt{305}}{2}
$