3x2+9=81

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Solution for 3x2+9=81 equation:



3x^2+9=81
We move all terms to the left:
3x^2+9-(81)=0
We add all the numbers together, and all the variables
3x^2-72=0
a = 3; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·3·(-72)
Δ = 864
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:
$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*3}=\frac{0-12\sqrt{6}}{6} =-\frac{12\sqrt{6}}{6} =-2\sqrt{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*3}=\frac{0+12\sqrt{6}}{6} =\frac{12\sqrt{6}}{6} =2\sqrt{6} $

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