2n2-6=42

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Solution for 2n2-6=42 equation:



2n^2-6=42
We move all terms to the left:
2n^2-6-(42)=0
We add all the numbers together, and all the variables
2n^2-48=0
a = 2; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·2·(-48)
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*2}=\frac{0-8\sqrt{6}}{4} =-\frac{8\sqrt{6}}{4} =-2\sqrt{6} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*2}=\frac{0+8\sqrt{6}}{4} =\frac{8\sqrt{6}}{4} =2\sqrt{6} $

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