x^2+50-5000=0

Solution for x^2+50-5000=0 equation:

x^2+50-5000=0

We add all the numbers together, and all the variables

x^2-4950=0

a = 1; b = 0; c = -4950;
Δ = b2-4ac
Δ = 02-4·1·(-4950)
Δ = 19800
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:

$\sqrt{\Delta}=\sqrt{19800}=\sqrt{900*22}=\sqrt{900}*\sqrt{22}=30\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{22}}{2*1}=\frac{0-30\sqrt{22}}{2}
=-\frac{30\sqrt{22}}{2}
=-15\sqrt{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{22}}{2*1}=\frac{0+30\sqrt{22}}{2}
=\frac{30\sqrt{22}}{2}
=15\sqrt{22}
$