84=x2+6

Solution for 84=x2+6 equation:

84=x2+6

We move all terms to the left:

84-(x2+6)=0

We add all the numbers together, and all the variables

-(+x^2+6)+84=0

We get rid of parentheses

-x^2-6+84=0

We add all the numbers together, and all the variables

-1x^2+78=0

a = -1; b = 0; c = +78;
Δ = b2-4ac
Δ = 02-4·(-1)·78
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*-1}=\frac{0-2\sqrt{78}}{-2}
=-\frac{2\sqrt{78}}{-2}
=-\frac{\sqrt{78}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*-1}=\frac{0+2\sqrt{78}}{-2}
=\frac{2\sqrt{78}}{-2}
=\frac{\sqrt{78}}{-1}
$