x^2-400-14700=0

Solution for x^2-400-14700=0 equation:

x^2-400-14700=0

We add all the numbers together, and all the variables

x^2-15100=0

a = 1; b = 0; c = -15100;
Δ = b2-4ac
Δ = 02-4·1·(-15100)
Δ = 60400
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:

$\sqrt{\Delta}=\sqrt{60400}=\sqrt{400*151}=\sqrt{400}*\sqrt{151}=20\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{151}}{2*1}=\frac{0-20\sqrt{151}}{2}
=-\frac{20\sqrt{151}}{2}
=-10\sqrt{151}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{151}}{2*1}=\frac{0+20\sqrt{151}}{2}
=\frac{20\sqrt{151}}{2}
=10\sqrt{151}
$