96=2x*x-1

Solution for 96=2x*x-1 equation:

96=2x*x-1

We move all terms to the left:

96-(2x*x-1)=0

We get rid of parentheses

-2x*x+1+96=0

We add all the numbers together, and all the variables

-2x*x+97=0

Wy multiply elements

-2x^2+97=0

a = -2; b = 0; c = +97;
Δ = b2-4ac
Δ = 02-4·(-2)·97
Δ = 776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{194}}{2*-2}=\frac{0-2\sqrt{194}}{-4}
=-\frac{2\sqrt{194}}{-4}
=-\frac{\sqrt{194}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{194}}{2*-2}=\frac{0+2\sqrt{194}}{-4}
=\frac{2\sqrt{194}}{-4}
=\frac{\sqrt{194}}{-2}
$