(X+5)(x+9)=126

Solution for (X+5)(x+9)=126 equation:

(X+5)(X+9)=126

We move all terms to the left:

(X+5)(X+9)-(126)=0

We multiply parentheses ..

(+X^2+9X+5X+45)-126=0

We get rid of parentheses

X^2+9X+5X+45-126=0

We add all the numbers together, and all the variables

X^2+14X-81=0

a = 1; b = 14; c = -81;
Δ = b2-4ac
Δ = 142-4·1·(-81)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{130}}{2*1}=\frac{-14-2\sqrt{130}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{130}}{2*1}=\frac{-14+2\sqrt{130}}{2}
$