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6x^2-363x+121=0
a = 6; b = -363; c = +121;
Δ = b2-4ac
Δ = -3632-4·6·121
Δ = 128865
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{128865}=\sqrt{121*1065}=\sqrt{121}*\sqrt{1065}=11\sqrt{1065}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-363)-11\sqrt{1065}}{2*6}=\frac{363-11\sqrt{1065}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-363)+11\sqrt{1065}}{2*6}=\frac{363+11\sqrt{1065}}{12} $
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