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14000x^2-40500x-18500=0
a = 14000; b = -40500; c = -18500;
Δ = b2-4ac
Δ = -405002-4·14000·(-18500)
Δ = 2676250000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2676250000}=\sqrt{250000*10705}=\sqrt{250000}*\sqrt{10705}=500\sqrt{10705}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40500)-500\sqrt{10705}}{2*14000}=\frac{40500-500\sqrt{10705}}{28000} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40500)+500\sqrt{10705}}{2*14000}=\frac{40500+500\sqrt{10705}}{28000} $
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