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2x^2-2x-121=0
a = 2; b = -2; c = -121;
Δ = b2-4ac
Δ = -22-4·2·(-121)
Δ = 972
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18\sqrt{3}}{2*2}=\frac{2-18\sqrt{3}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18\sqrt{3}}{2*2}=\frac{2+18\sqrt{3}}{4} $
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