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

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

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

We multiply parentheses ..

(+16x^2-24x-2x+3)=0

We get rid of parentheses

16x^2-24x-2x+3=0

We add all the numbers together, and all the variables

16x^2-26x+3=0

a = 16; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·16·3
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-22}{2*16}=\frac{4}{32}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+22}{2*16}=\frac{48}{32}
=1+1/2
$