2x^2-1=40

Solution for 2x^2-1=40 equation:

2x^2-1=40

We move all terms to the left:

2x^2-1-(40)=0

We add all the numbers together, and all the variables

2x^2-41=0

a = 2; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·2·(-41)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{82}}{2*2}=\frac{0-2\sqrt{82}}{4}
=-\frac{2\sqrt{82}}{4}
=-\frac{\sqrt{82}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{82}}{2*2}=\frac{0+2\sqrt{82}}{4}
=\frac{2\sqrt{82}}{4}
=\frac{\sqrt{82}}{2}
$