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0.5x^2-9x+4.5=0
a = 0.5; b = -9; c = +4.5;
Δ = b2-4ac
Δ = -92-4·0.5·4.5
Δ = 72
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-6\sqrt{2}}{2*0.5}=\frac{9-6\sqrt{2}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+6\sqrt{2}}{2*0.5}=\frac{9+6\sqrt{2}}{1} $
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