(4x-3)(2x-8)=0

Solution for (4x-3)(2x-8)=0 equation:

(4x-3)(2x-8)=0

We multiply parentheses ..

(+8x^2-32x-6x+24)=0

We get rid of parentheses

8x^2-32x-6x+24=0

We add all the numbers together, and all the variables

8x^2-38x+24=0

a = 8; b = -38; c = +24;
Δ = b2-4ac
Δ = -382-4·8·24
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-26}{2*8}=\frac{12}{16}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+26}{2*8}=\frac{64}{16}
=4
$