(4x-5)(6x-8)=0

Solution for (4x-5)(6x-8)=0 equation:

(4x-5)(6x-8)=0

We multiply parentheses ..

(+24x^2-32x-30x+40)=0

We get rid of parentheses

24x^2-32x-30x+40=0

We add all the numbers together, and all the variables

24x^2-62x+40=0

a = 24; b = -62; c = +40;
Δ = b2-4ac
Δ = -622-4·24·40
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-2}{2*24}=\frac{60}{48}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+2}{2*24}=\frac{64}{48}
=1+1/3
$