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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

a = 1; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·1·(-36)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*1}=\frac{12}{2}
=6
$