3n^2+8=83

Solution for 3n^2+8=83 equation:

3n^2+8=83

We move all terms to the left:

3n^2+8-(83)=0

We add all the numbers together, and all the variables

3n^2-75=0

a = 3; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·3·(-75)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*3}=\frac{-30}{6}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*3}=\frac{30}{6}
=5
$