(3x-5)(8x-9)=0

Solution for (3x-5)(8x-9)=0 equation:

(3x-5)(8x-9)=0

We multiply parentheses ..

(+24x^2-27x-40x+45)=0

We get rid of parentheses

24x^2-27x-40x+45=0

We add all the numbers together, and all the variables

24x^2-67x+45=0

a = 24; b = -67; c = +45;
Δ = b2-4ac
Δ = -672-4·24·45
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{-(-67)-13}{2*24}=\frac{54}{48}
=1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+13}{2*24}=\frac{80}{48}
=1+2/3
$