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9x^2-155x+500=0
a = 9; b = -155; c = +500;
Δ = b2-4ac
Δ = -1552-4·9·500
Δ = 6025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-155)-5\sqrt{241}}{2*9}=\frac{155-5\sqrt{241}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+5\sqrt{241}}{2*9}=\frac{155+5\sqrt{241}}{18} $
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