3x^2-2=187

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Solution for 3x^2-2=187 equation:



3x^2-2=187
We move all terms to the left:
3x^2-2-(187)=0
We add all the numbers together, and all the variables
3x^2-189=0
a = 3; b = 0; c = -189;
Δ = b2-4ac
Δ = 02-4·3·(-189)
Δ = 2268
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:
$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{7}}{2*3}=\frac{0-18\sqrt{7}}{6} =-\frac{18\sqrt{7}}{6} =-3\sqrt{7} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{7}}{2*3}=\frac{0+18\sqrt{7}}{6} =\frac{18\sqrt{7}}{6} =3\sqrt{7} $

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