684=4x2+8

Solution for 684=4x2+8 equation:

684=4x^2+8

We move all terms to the left:

684-(4x^2+8)=0

We get rid of parentheses

-4x^2-8+684=0

We add all the numbers together, and all the variables

-4x^2+676=0

a = -4; b = 0; c = +676;
Δ = b2-4ac
Δ = 02-4·(-4)·676
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-104}{2*-4}=\frac{-104}{-8}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+104}{2*-4}=\frac{104}{-8}
=-13
$