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12x^2-48x-24=0
a = 12; b = -48; c = -24;
Δ = b2-4ac
Δ = -482-4·12·(-24)
Δ = 3456
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{6}}{2*12}=\frac{48-24\sqrt{6}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{6}}{2*12}=\frac{48+24\sqrt{6}}{24} $
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