(8n-1)(2n+5)=0

Solution for (8n-1)(2n+5)=0 equation:

(8n-1)(2n+5)=0

We multiply parentheses ..

(+16n^2+40n-2n-5)=0

We get rid of parentheses

16n^2+40n-2n-5=0

We add all the numbers together, and all the variables

16n^2+38n-5=0

a = 16; b = 38; c = -5;
Δ = b2-4ac
Δ = 382-4·16·(-5)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-42}{2*16}=\frac{-80}{32}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+42}{2*16}=\frac{4}{32}
=1/8
$