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51(x-9)x0.5=918
We move all terms to the left:
51(x-9)x0.5-(918)=0
We multiply parentheses
51x^2-459x-918=0
a = 51; b = -459; c = -918;
Δ = b2-4ac
Δ = -4592-4·51·(-918)
Δ = 397953
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{397953}=\sqrt{23409*17}=\sqrt{23409}*\sqrt{17}=153\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-459)-153\sqrt{17}}{2*51}=\frac{459-153\sqrt{17}}{102} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-459)+153\sqrt{17}}{2*51}=\frac{459+153\sqrt{17}}{102} $
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