(4n-1)(8n-7)=0

Solution for (4n-1)(8n-7)=0 equation:

(4n-1)(8n-7)=0

We multiply parentheses ..

(+32n^2-28n-8n+7)=0

We get rid of parentheses

32n^2-28n-8n+7=0

We add all the numbers together, and all the variables

32n^2-36n+7=0

a = 32; b = -36; c = +7;
Δ = b2-4ac
Δ = -362-4·32·7
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20}{2*32}=\frac{16}{64}
=1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20}{2*32}=\frac{56}{64}
=7/8
$