6x^2+1=97

Solution for 6x^2+1=97 equation:

6x^2+1=97

We move all terms to the left:

6x^2+1-(97)=0

We add all the numbers together, and all the variables

6x^2-96=0

a = 6; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·6·(-96)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*6}=\frac{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*6}=\frac{48}{12}
=4
$