x^2+8=8000

Solution for x^2+8=8000 equation:

x^2+8=8000

We move all terms to the left:

x^2+8-(8000)=0

We add all the numbers together, and all the variables

x^2-7992=0

a = 1; b = 0; c = -7992;
Δ = b2-4ac
Δ = 02-4·1·(-7992)
Δ = 31968
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:

$\sqrt{\Delta}=\sqrt{31968}=\sqrt{144*222}=\sqrt{144}*\sqrt{222}=12\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{222}}{2*1}=\frac{0-12\sqrt{222}}{2}
=-\frac{12\sqrt{222}}{2}
=-6\sqrt{222}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{222}}{2*1}=\frac{0+12\sqrt{222}}{2}
=\frac{12\sqrt{222}}{2}
=6\sqrt{222}
$