x*x=420

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Solution for x*x=420 equation:



x*x=420
We move all terms to the left:
x*x-(420)=0
Wy multiply elements
x^2-420=0
a = 1; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·1·(-420)
Δ = 1680
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:
$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*1}=\frac{0-4\sqrt{105}}{2} =-\frac{4\sqrt{105}}{2} =-2\sqrt{105} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*1}=\frac{0+4\sqrt{105}}{2} =\frac{4\sqrt{105}}{2} =2\sqrt{105} $

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