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6x^2+300x-5000=0
a = 6; b = 300; c = -5000;
Δ = b2-4ac
Δ = 3002-4·6·(-5000)
Δ = 210000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{210000}=\sqrt{10000*21}=\sqrt{10000}*\sqrt{21}=100\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-100\sqrt{21}}{2*6}=\frac{-300-100\sqrt{21}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+100\sqrt{21}}{2*6}=\frac{-300+100\sqrt{21}}{12} $
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