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x2-9x-11=0
We add all the numbers together, and all the variables
x^2-9x-11=0
a = 1; b = -9; c = -11;
Δ = b2-4ac
Δ = -92-4·1·(-11)
Δ = 125
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5\sqrt{5}}{2*1}=\frac{9-5\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5\sqrt{5}}{2*1}=\frac{9+5\sqrt{5}}{2} $
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