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x^2-17x-16=3
We move all terms to the left:
x^2-17x-16-(3)=0
We add all the numbers together, and all the variables
x^2-17x-19=0
a = 1; b = -17; c = -19;
Δ = b2-4ac
Δ = -172-4·1·(-19)
Δ = 365
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{365}}{2*1}=\frac{17-\sqrt{365}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{365}}{2*1}=\frac{17+\sqrt{365}}{2} $
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