8n(n+3)=2n-5

Solution for 8n(n+3)=2n-5 equation:

8n(n+3)=2n-5

We move all terms to the left:

8n(n+3)-(2n-5)=0

We multiply parentheses

8n^2+24n-(2n-5)=0

We get rid of parentheses

8n^2+24n-2n+5=0

We add all the numbers together, and all the variables

8n^2+22n+5=0

a = 8; b = 22; c = +5;
Δ = b2-4ac
Δ = 222-4·8·5
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-18}{2*8}=\frac{-40}{16}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+18}{2*8}=\frac{-4}{16}
=-1/4
$