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

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

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

We multiply parentheses ..

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

We multiply parentheses

5x^2-45x+20x-180=0

We add all the numbers together, and all the variables

5x^2-25x-180=0

a = 5; b = -25; c = -180;
Δ = b2-4ac
Δ = -252-4·5·(-180)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-65}{2*5}=\frac{-40}{10}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+65}{2*5}=\frac{90}{10}
=9
$