(x+4)(x+9)=76

Solution for (x+4)(x+9)=76 equation:

(x+4)(x+9)=76

We move all terms to the left:

(x+4)(x+9)-(76)=0

We multiply parentheses ..

(+x^2+9x+4x+36)-76=0

We get rid of parentheses

x^2+9x+4x+36-76=0

We add all the numbers together, and all the variables

x^2+13x-40=0

a = 1; b = 13; c = -40;
Δ = b2-4ac
Δ = 132-4·1·(-40)
Δ = 329
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{-(13)-\sqrt{329}}{2*1}=\frac{-13-\sqrt{329}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{329}}{2*1}=\frac{-13+\sqrt{329}}{2}
$