(5x-8)(4x-9)=0

Solution for (5x-8)(4x-9)=0 equation:

(5x-8)(4x-9)=0

We multiply parentheses ..

(+20x^2-45x-32x+72)=0

We get rid of parentheses

20x^2-45x-32x+72=0

We add all the numbers together, and all the variables

20x^2-77x+72=0

a = 20; b = -77; c = +72;
Δ = b2-4ac
Δ = -772-4·20·72
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-13}{2*20}=\frac{64}{40}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+13}{2*20}=\frac{90}{40}
=2+1/4
$