(5x-6)(8x-9)=0

Solution for (5x-6)(8x-9)=0 equation:

(5x-6)(8x-9)=0

We multiply parentheses ..

(+40x^2-45x-48x+54)=0

We get rid of parentheses

40x^2-45x-48x+54=0

We add all the numbers together, and all the variables

40x^2-93x+54=0

a = 40; b = -93; c = +54;
Δ = b2-4ac
Δ = -932-4·40·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-93)-3}{2*40}=\frac{90}{80}
=1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+3}{2*40}=\frac{96}{80}
=1+1/5
$