14=8x^2+1

Solution for 14=8x^2+1 equation:

14=8x^2+1

We move all terms to the left:

14-(8x^2+1)=0

We get rid of parentheses

-8x^2-1+14=0

We add all the numbers together, and all the variables

-8x^2+13=0

a = -8; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-8)·13
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*-8}=\frac{0-4\sqrt{26}}{-16}
=-\frac{4\sqrt{26}}{-16}
=-\frac{\sqrt{26}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*-8}=\frac{0+4\sqrt{26}}{-16}
=\frac{4\sqrt{26}}{-16}
=\frac{\sqrt{26}}{-4}
$