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6x^2-57x-36=0
a = 6; b = -57; c = -36;
Δ = b2-4ac
Δ = -572-4·6·(-36)
Δ = 4113
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4113}=\sqrt{9*457}=\sqrt{9}*\sqrt{457}=3\sqrt{457}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{457}}{2*6}=\frac{57-3\sqrt{457}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{457}}{2*6}=\frac{57+3\sqrt{457}}{12} $
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