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

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

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

We add all the numbers together, and all the variables

(4x+5)(-1x-9)=0

We multiply parentheses ..

(-4x^2-36x-5x-45)=0

We get rid of parentheses

-4x^2-36x-5x-45=0

We add all the numbers together, and all the variables

-4x^2-41x-45=0

a = -4; b = -41; c = -45;
Δ = b2-4ac
Δ = -412-4·(-4)·(-45)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-31}{2*-4}=\frac{10}{-8}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+31}{2*-4}=\frac{72}{-8}
=-9
$