100x^2-83=0

Solution for 100x^2-83=0 equation:

100x^2-83=0

a = 100; b = 0; c = -83;
Δ = b2-4ac
Δ = 02-4·100·(-83)
Δ = 33200
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:

$\sqrt{\Delta}=\sqrt{33200}=\sqrt{400*83}=\sqrt{400}*\sqrt{83}=20\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{83}}{2*100}=\frac{0-20\sqrt{83}}{200}
=-\frac{20\sqrt{83}}{200}
=-\frac{\sqrt{83}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{83}}{2*100}=\frac{0+20\sqrt{83}}{200}
=\frac{20\sqrt{83}}{200}
=\frac{\sqrt{83}}{10}
$