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11x^2-74x-126=0
a = 11; b = -74; c = -126;
Δ = b2-4ac
Δ = -742-4·11·(-126)
Δ = 11020
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11020}=\sqrt{4*2755}=\sqrt{4}*\sqrt{2755}=2\sqrt{2755}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{2755}}{2*11}=\frac{74-2\sqrt{2755}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{2755}}{2*11}=\frac{74+2\sqrt{2755}}{22} $
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