2(4n2+17)=234

Solution for 2(4n2+17)=234 equation:

2(4n^2+17)=234

We move all terms to the left:

2(4n^2+17)-(234)=0

We multiply parentheses

8n^2+34-234=0

We add all the numbers together, and all the variables

8n^2-200=0

a = 8; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·8·(-200)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*8}=\frac{-80}{16}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*8}=\frac{80}{16}
=5
$