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6x^2-6x-4780=0
a = 6; b = -6; c = -4780;
Δ = b2-4ac
Δ = -62-4·6·(-4780)
Δ = 114756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{114756}=\sqrt{4*28689}=\sqrt{4}*\sqrt{28689}=2\sqrt{28689}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{28689}}{2*6}=\frac{6-2\sqrt{28689}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{28689}}{2*6}=\frac{6+2\sqrt{28689}}{12} $
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