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6x^2+54x-32=0
a = 6; b = 54; c = -32;
Δ = b2-4ac
Δ = 542-4·6·(-32)
Δ = 3684
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3684}=\sqrt{4*921}=\sqrt{4}*\sqrt{921}=2\sqrt{921}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{921}}{2*6}=\frac{-54-2\sqrt{921}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{921}}{2*6}=\frac{-54+2\sqrt{921}}{12} $
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