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100x^2-200x+50=0
a = 100; b = -200; c = +50;
Δ = b2-4ac
Δ = -2002-4·100·50
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{-(-200)-100\sqrt{2}}{2*100}=\frac{200-100\sqrt{2}}{200} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+100\sqrt{2}}{2*100}=\frac{200+100\sqrt{2}}{200} $
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