(4x+9)(5x-12)=0

Solution for (4x+9)(5x-12)=0 equation:

(4x+9)(5x-12)=0

We multiply parentheses ..

(+20x^2-48x+45x-108)=0

We get rid of parentheses

20x^2-48x+45x-108=0

We add all the numbers together, and all the variables

20x^2-3x-108=0

a = 20; b = -3; c = -108;
Δ = b2-4ac
Δ = -32-4·20·(-108)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-93}{2*20}=\frac{-90}{40}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+93}{2*20}=\frac{96}{40}
=2+2/5
$