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x^2+9-486=0

We add all the numbers together, and all the variables

x^2-477=0

a = 1; b = 0; c = -477;

Δ = b^{2}-4ac

Δ = 0^{2}-4·1·(-477)

Δ = 1908

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{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{53}}{2*1}=\frac{0-6\sqrt{53}}{2} =-\frac{6\sqrt{53}}{2} =-3\sqrt{53} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{53}}{2*1}=\frac{0+6\sqrt{53}}{2} =\frac{6\sqrt{53}}{2} =3\sqrt{53} $

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