x^2+8=84

Solution for x^2+8=84 equation:

x^2+8=84

We move all terms to the left:

x^2+8-(84)=0

We add all the numbers together, and all the variables

x^2-76=0

a = 1; b = 0; c = -76;
Δ = b2-4ac
Δ = 02-4·1·(-76)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{19}}{2*1}=\frac{0-4\sqrt{19}}{2}
=-\frac{4\sqrt{19}}{2}
=-2\sqrt{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{19}}{2*1}=\frac{0+4\sqrt{19}}{2}
=\frac{4\sqrt{19}}{2}
=2\sqrt{19}
$