5(x+2)(x-9)=0

Solution for 5(x+2)(x-9)=0 equation:

5(x+2)(x-9)=0

We multiply parentheses ..

5(+x^2-9x+2x-18)=0

We multiply parentheses

5x^2-45x+10x-90=0

We add all the numbers together, and all the variables

5x^2-35x-90=0

a = 5; b = -35; c = -90;
Δ = b2-4ac
Δ = -352-4·5·(-90)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-55}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+55}{2*5}=\frac{90}{10}
=9
$