(3x-5)(6x-8)=0

Solution for (3x-5)(6x-8)=0 equation:

(3x-5)(6x-8)=0

We multiply parentheses ..

(+18x^2-24x-30x+40)=0

We get rid of parentheses

18x^2-24x-30x+40=0

We add all the numbers together, and all the variables

18x^2-54x+40=0

a = 18; b = -54; c = +40;
Δ = b2-4ac
Δ = -542-4·18·40
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6}{2*18}=\frac{48}{36}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6}{2*18}=\frac{60}{36}
=1+2/3
$