6x^2-14=34.

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Solution for 6x^2-14=34. equation:



6x^2-14=34.
We move all terms to the left:
6x^2-14-(34.)=0
We add all the numbers together, and all the variables
6x^2-14-34=0
We add all the numbers together, and all the variables
6x^2-48=0
a = 6; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·6·(-48)
Δ = 1152
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:
$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*6}=\frac{0-24\sqrt{2}}{12} =-\frac{24\sqrt{2}}{12} =-2\sqrt{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*6}=\frac{0+24\sqrt{2}}{12} =\frac{24\sqrt{2}}{12} =2\sqrt{2} $

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