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x^2-9x-16=2
We move all terms to the left:
x^2-9x-16-(2)=0
We add all the numbers together, and all the variables
x^2-9x-18=0
a = 1; b = -9; c = -18;
Δ = b2-4ac
Δ = -92-4·1·(-18)
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{17}}{2*1}=\frac{9-3\sqrt{17}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{17}}{2*1}=\frac{9+3\sqrt{17}}{2} $
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