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-6x^2+24x+16=0
a = -6; b = 24; c = +16;
Δ = b2-4ac
Δ = 242-4·(-6)·16
Δ = 960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{15}}{2*-6}=\frac{-24-8\sqrt{15}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{15}}{2*-6}=\frac{-24+8\sqrt{15}}{-12} $
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