2x^2-1=195

Solution for 2x^2-1=195 equation:

2x^2-1=195

We move all terms to the left:

2x^2-1-(195)=0

We add all the numbers together, and all the variables

2x^2-196=0

a = 2; b = 0; c = -196;
Δ = b2-4ac
Δ = 02-4·2·(-196)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*2}=\frac{0-28\sqrt{2}}{4}
=-\frac{28\sqrt{2}}{4}
=-7\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*2}=\frac{0+28\sqrt{2}}{4}
=\frac{28\sqrt{2}}{4}
=7\sqrt{2}
$