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12x^2-6x-52=0
a = 12; b = -6; c = -52;
Δ = b2-4ac
Δ = -62-4·12·(-52)
Δ = 2532
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2532}=\sqrt{4*633}=\sqrt{4}*\sqrt{633}=2\sqrt{633}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{633}}{2*12}=\frac{6-2\sqrt{633}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{633}}{2*12}=\frac{6+2\sqrt{633}}{24} $
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