x^2+6=60

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Solution for x^2+6=60 equation:



x^2+6=60
We move all terms to the left:
x^2+6-(60)=0
We add all the numbers together, and all the variables
x^2-54=0
a = 1; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·1·(-54)
Δ = 216
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:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*1}=\frac{0-6\sqrt{6}}{2} =-\frac{6\sqrt{6}}{2} =-3\sqrt{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*1}=\frac{0+6\sqrt{6}}{2} =\frac{6\sqrt{6}}{2} =3\sqrt{6} $

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