(x+5)(x+9)=20

Solution for (x+5)(x+9)=20 equation:

(x+5)(x+9)=20

We move all terms to the left:

(x+5)(x+9)-(20)=0

We multiply parentheses ..

(+x^2+9x+5x+45)-20=0

We get rid of parentheses

x^2+9x+5x+45-20=0

We add all the numbers together, and all the variables

x^2+14x+25=0

a = 1; b = 14; c = +25;
Δ = b2-4ac
Δ = 142-4·1·25
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{6}}{2*1}=\frac{-14-4\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{6}}{2*1}=\frac{-14+4\sqrt{6}}{2}
$