(-4x+9)(-6x-5)=0

Solution for (-4x+9)(-6x-5)=0 equation:

(-4x+9)(-6x-5)=0

We multiply parentheses ..

(+24x^2+20x-54x-45)=0

We get rid of parentheses

24x^2+20x-54x-45=0

We add all the numbers together, and all the variables

24x^2-34x-45=0

a = 24; b = -34; c = -45;
Δ = b2-4ac
Δ = -342-4·24·(-45)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-74}{2*24}=\frac{-40}{48}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+74}{2*24}=\frac{108}{48}
=2+1/4
$