(x+4)(x+9)+5x=0

Solution for (x+4)(x+9)+5x=0 equation:

(x+4)(x+9)+5x=0

We add all the numbers together, and all the variables

5x+(x+4)(x+9)=0

We multiply parentheses ..

(+x^2+9x+4x+36)+5x=0

We get rid of parentheses

x^2+9x+4x+5x+36=0

We add all the numbers together, and all the variables

x^2+18x+36=0

a = 1; b = 18; c = +36;
Δ = b2-4ac
Δ = 182-4·1·36
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{5}}{2*1}=\frac{-18-6\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{5}}{2*1}=\frac{-18+6\sqrt{5}}{2}
$