X^2-300x+200=0

Solution for X^2-300x+200=0 equation:

X^2-300X+200=0

a = 1; b = -300; c = +200;
Δ = b2-4ac
Δ = -3002-4·1·200
Δ = 89200
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:

$\sqrt{\Delta}=\sqrt{89200}=\sqrt{400*223}=\sqrt{400}*\sqrt{223}=20\sqrt{223}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-20\sqrt{223}}{2*1}=\frac{300-20\sqrt{223}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+20\sqrt{223}}{2*1}=\frac{300+20\sqrt{223}}{2}
$