50x2-100=0

Solution for 50x2-100=0 equation:

50x^2-100=0

a = 50; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·50·(-100)
Δ = 20000
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:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{2}}{2*50}=\frac{0-100\sqrt{2}}{100}
=-\frac{100\sqrt{2}}{100}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{2}}{2*50}=\frac{0+100\sqrt{2}}{100}
=\frac{100\sqrt{2}}{100}
=\sqrt{2}
$