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(X)2-8X=121.5
We move all terms to the left:
(X)2-8X-(121.5)=0
We add all the numbers together, and all the variables
X^2-8X-121.5=0
a = 1; b = -8; c = -121.5;
Δ = b2-4ac
Δ = -82-4·1·(-121.5)
Δ = 550
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{550}=\sqrt{25*22}=\sqrt{25}*\sqrt{22}=5\sqrt{22}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-5\sqrt{22}}{2*1}=\frac{8-5\sqrt{22}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+5\sqrt{22}}{2*1}=\frac{8+5\sqrt{22}}{2} $
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