3+5n=1+8n2

Solution for 3+5n=1+8n2 equation:

3+5n=1+8n^2

We move all terms to the left:

3+5n-(1+8n^2)=0

We get rid of parentheses

-8n^2+5n-1+3=0

We add all the numbers together, and all the variables

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

a = -8; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-8)·2
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{89}}{2*-8}=\frac{-5-\sqrt{89}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*-8}=\frac{-5+\sqrt{89}}{-16}
$