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6x^2-920x+2400=0
a = 6; b = -920; c = +2400;
Δ = b2-4ac
Δ = -9202-4·6·2400
Δ = 788800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{788800}=\sqrt{1600*493}=\sqrt{1600}*\sqrt{493}=40\sqrt{493}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-920)-40\sqrt{493}}{2*6}=\frac{920-40\sqrt{493}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-920)+40\sqrt{493}}{2*6}=\frac{920+40\sqrt{493}}{12} $
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