(X+5)(x+9)=129

Solution for (X+5)(x+9)=129 equation:

(X+5)(X+9)=129

We move all terms to the left:

(X+5)(X+9)-(129)=0

We multiply parentheses ..

(+X^2+9X+5X+45)-129=0

We get rid of parentheses

X^2+9X+5X+45-129=0

We add all the numbers together, and all the variables

X^2+14X-84=0

a = 1; b = 14; c = -84;
Δ = b2-4ac
Δ = 142-4·1·(-84)
Δ = 532
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{133}}{2*1}=\frac{-14-2\sqrt{133}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{133}}{2*1}=\frac{-14+2\sqrt{133}}{2}
$