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6x^2-2x-57=0
a = 6; b = -2; c = -57;
Δ = b2-4ac
Δ = -22-4·6·(-57)
Δ = 1372
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14\sqrt{7}}{2*6}=\frac{2-14\sqrt{7}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14\sqrt{7}}{2*6}=\frac{2+14\sqrt{7}}{12} $
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