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x^2-22x+73=0
a = 1; b = -22; c = +73;
Δ = b2-4ac
Δ = -222-4·1·73
Δ = 192
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8\sqrt{3}}{2*1}=\frac{22-8\sqrt{3}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8\sqrt{3}}{2*1}=\frac{22+8\sqrt{3}}{2} $
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