4n^2-2=194

Solution for 4n^2-2=194 equation:

4n^2-2=194

We move all terms to the left:

4n^2-2-(194)=0

We add all the numbers together, and all the variables

4n^2-196=0

a = 4; b = 0; c = -196;
Δ = b2-4ac
Δ = 02-4·4·(-196)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56}{2*4}=\frac{-56}{8}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56}{2*4}=\frac{56}{8}
=7
$