(4x-3)(8x-5)=0

Solution for (4x-3)(8x-5)=0 equation:

(4x-3)(8x-5)=0

We multiply parentheses ..

(+32x^2-20x-24x+15)=0

We get rid of parentheses

32x^2-20x-24x+15=0

We add all the numbers together, and all the variables

32x^2-44x+15=0

a = 32; b = -44; c = +15;
Δ = b2-4ac
Δ = -442-4·32·15
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4}{2*32}=\frac{40}{64}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4}{2*32}=\frac{48}{64}
=3/4
$