(4a-3)(8a+2)=0

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

(4a-3)(8a+2)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

32a^2-16a-6=0

a = 32; b = -16; c = -6;
Δ = b2-4ac
Δ = -162-4·32·(-6)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-32}{2*32}=\frac{-16}{64}
=-1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+32}{2*32}=\frac{48}{64}
=3/4
$