2x^2+1=31

Solution for 2x^2+1=31 equation:

2x^2+1=31

We move all terms to the left:

2x^2+1-(31)=0

We add all the numbers together, and all the variables

2x^2-30=0

a = 2; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·2·(-30)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*2}=\frac{0-4\sqrt{15}}{4}
=-\frac{4\sqrt{15}}{4}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*2}=\frac{0+4\sqrt{15}}{4}
=\frac{4\sqrt{15}}{4}
=\sqrt{15}
$