208333x^2-212500x+36500=0

Solution for 208333x^2-212500x+36500=0 equation:

208333x^2-212500x+36500=0

a = 208333; b = -212500; c = +36500;
Δ = b2-4ac
Δ = -2125002-4·208333·36500
Δ = 14739632000
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:

$\sqrt{\Delta}=\sqrt{14739632000}=\sqrt{1600*9212270}=\sqrt{1600}*\sqrt{9212270}=40\sqrt{9212270}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-212500)-40\sqrt{9212270}}{2*208333}=\frac{212500-40\sqrt{9212270}}{416666}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-212500)+40\sqrt{9212270}}{2*208333}=\frac{212500+40\sqrt{9212270}}{416666}
$