6x^2+23=201

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Solution for 6x^2+23=201 equation:



6x^2+23=201
We move all terms to the left:
6x^2+23-(201)=0
We add all the numbers together, and all the variables
6x^2-178=0
a = 6; b = 0; c = -178;
Δ = b2-4ac
Δ = 02-4·6·(-178)
Δ = 4272
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:
$\sqrt{\Delta}=\sqrt{4272}=\sqrt{16*267}=\sqrt{16}*\sqrt{267}=4\sqrt{267}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{267}}{2*6}=\frac{0-4\sqrt{267}}{12} =-\frac{4\sqrt{267}}{12} =-\frac{\sqrt{267}}{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{267}}{2*6}=\frac{0+4\sqrt{267}}{12} =\frac{4\sqrt{267}}{12} =\frac{\sqrt{267}}{3} $

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