(3x-1)(8x-2)=0

Solution for (3x-1)(8x-2)=0 equation:

(3x-1)(8x-2)=0

We multiply parentheses ..

(+24x^2-6x-8x+2)=0

We get rid of parentheses

24x^2-6x-8x+2=0

We add all the numbers together, and all the variables

24x^2-14x+2=0

a = 24; b = -14; c = +2;
Δ = b2-4ac
Δ = -142-4·24·2
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{-(-14)-2}{2*24}=\frac{12}{48}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*24}=\frac{16}{48}
=1/3
$