x^2+27-520=0

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Solution for x^2+27-520=0 equation:



x^2+27-520=0
We add all the numbers together, and all the variables
x^2-493=0
a = 1; b = 0; c = -493;
Δ = b2-4ac
Δ = 02-4·1·(-493)
Δ = 1972
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:
$\sqrt{\Delta}=\sqrt{1972}=\sqrt{4*493}=\sqrt{4}*\sqrt{493}=2\sqrt{493}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{493}}{2*1}=\frac{0-2\sqrt{493}}{2} =-\frac{2\sqrt{493}}{2} =-\sqrt{493} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{493}}{2*1}=\frac{0+2\sqrt{493}}{2} =\frac{2\sqrt{493}}{2} =\sqrt{493} $

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