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

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

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

We multiply parentheses ..

(+8x^2-24x-1x+3)=0

We get rid of parentheses

8x^2-24x-1x+3=0

We add all the numbers together, and all the variables

8x^2-25x+3=0

a = 8; b = -25; c = +3;
Δ = b2-4ac
Δ = -252-4·8·3
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-23}{2*8}=\frac{2}{16}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+23}{2*8}=\frac{48}{16}
=3
$