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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

20x^2+21x-54=0

a = 20; b = 21; c = -54;
Δ = b2-4ac
Δ = 212-4·20·(-54)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-69}{2*20}=\frac{-90}{40}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+69}{2*20}=\frac{48}{40}
=1+1/5
$