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x^2-42x+73=0
a = 1; b = -42; c = +73;
Δ = b2-4ac
Δ = -422-4·1·73
Δ = 1472
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-8\sqrt{23}}{2*1}=\frac{42-8\sqrt{23}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+8\sqrt{23}}{2*1}=\frac{42+8\sqrt{23}}{2} $
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