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.5x^2+18x+9=0
a = .5; b = 18; c = +9;
Δ = b2-4ac
Δ = 182-4·.5·9
Δ = 306
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{306}=\sqrt{9*34}=\sqrt{9}*\sqrt{34}=3\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-3\sqrt{34}}{2*.5}=\frac{-18-3\sqrt{34}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+3\sqrt{34}}{2*.5}=\frac{-18+3\sqrt{34}}{1} $
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