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0.5x^2-500x+750=0
a = 0.5; b = -500; c = +750;
Δ = b2-4ac
Δ = -5002-4·0.5·750
Δ = 248500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{248500}=\sqrt{100*2485}=\sqrt{100}*\sqrt{2485}=10\sqrt{2485}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-10\sqrt{2485}}{2*0.5}=\frac{500-10\sqrt{2485}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+10\sqrt{2485}}{2*0.5}=\frac{500+10\sqrt{2485}}{1} $
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