2x^2-1=163

Solution for 2x^2-1=163 equation:

2x^2-1=163

We move all terms to the left:

2x^2-1-(163)=0

We add all the numbers together, and all the variables

2x^2-164=0

a = 2; b = 0; c = -164;
Δ = b2-4ac
Δ = 02-4·2·(-164)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{82}}{2*2}=\frac{0-4\sqrt{82}}{4}
=-\frac{4\sqrt{82}}{4}
=-\sqrt{82}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{82}}{2*2}=\frac{0+4\sqrt{82}}{4}
=\frac{4\sqrt{82}}{4}
=\sqrt{82}
$