2x^2-61=1

Solution for 2x^2-61=1 equation:

2x^2-61=1

We move all terms to the left:

2x^2-61-(1)=0

We add all the numbers together, and all the variables

2x^2-62=0

a = 2; b = 0; c = -62;
Δ = b2-4ac
Δ = 02-4·2·(-62)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{31}}{2*2}=\frac{0-4\sqrt{31}}{4}
=-\frac{4\sqrt{31}}{4}
=-\sqrt{31}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{31}}{2*2}=\frac{0+4\sqrt{31}}{4}
=\frac{4\sqrt{31}}{4}
=\sqrt{31}
$