320x^2-36900x+200000=0

Solution for 320x^2-36900x+200000=0 equation:

320x^2-36900x+200000=0

a = 320; b = -36900; c = +200000;
Δ = b2-4ac
Δ = -369002-4·320·200000
Δ = 1105610000
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:

$\sqrt{\Delta}=\sqrt{1105610000}=\sqrt{5290000*209}=\sqrt{5290000}*\sqrt{209}=2300\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36900)-2300\sqrt{209}}{2*320}=\frac{36900-2300\sqrt{209}}{640}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36900)+2300\sqrt{209}}{2*320}=\frac{36900+2300\sqrt{209}}{640}
$