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

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

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

We move all terms to the left:

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

We multiply parentheses

8n^2+16n-(2n-5)=0

We get rid of parentheses

8n^2+16n-2n+5=0

We add all the numbers together, and all the variables

8n^2+14n+5=0

a = 8; b = 14; c = +5;
Δ = b2-4ac
Δ = 142-4·8·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6}{2*8}=\frac{-20}{16}
=-1+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*8}=\frac{-8}{16}
=-1/2
$