2(6^2a+4)-8=48

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Solution for 2(6^2a+4)-8=48 equation:



2(6^2a+4)-8=48
We move all terms to the left:
2(6^2a+4)-8-(48)=0
We add all the numbers together, and all the variables
2(6^2a+4)-56=0
We multiply parentheses
12a^2+8-56=0
We add all the numbers together, and all the variables
12a^2-48=0
a = 12; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·12·(-48)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*12}=\frac{-48}{24} =-2 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*12}=\frac{48}{24} =2 $

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