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x^2-18x+81=17+81
We move all terms to the left:
x^2-18x+81-(17+81)=0
We add all the numbers together, and all the variables
x^2-18x+81-98=0
We add all the numbers together, and all the variables
x^2-18x-17=0
a = 1; b = -18; c = -17;
Δ = b2-4ac
Δ = -182-4·1·(-17)
Δ = 392
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-14\sqrt{2}}{2*1}=\frac{18-14\sqrt{2}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14\sqrt{2}}{2*1}=\frac{18+14\sqrt{2}}{2} $
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