(2x+9)(4x-20)=0

Solution for (2x+9)(4x-20)=0 equation:

(2x+9)(4x-20)=0

We multiply parentheses ..

(+8x^2-40x+36x-180)=0

We get rid of parentheses

8x^2-40x+36x-180=0

We add all the numbers together, and all the variables

8x^2-4x-180=0

a = 8; b = -4; c = -180;
Δ = b2-4ac
Δ = -42-4·8·(-180)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-76}{2*8}=\frac{-72}{16}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+76}{2*8}=\frac{80}{16}
=5
$