(8/3)y=48

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Solution for (8/3)y=48 equation:



(8/3)y=48
We move all terms to the left:
(8/3)y-(48)=0
Domain of the equation: 3)y!=0
y!=0/1
y!=0
y∈R
We add all the numbers together, and all the variables
(+8/3)y-48=0
We multiply parentheses
8y^2-48=0
a = 8; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·8·(-48)
Δ = 1536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*8}=\frac{0-16\sqrt{6}}{16} =-\frac{16\sqrt{6}}{16} =-\sqrt{6} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*8}=\frac{0+16\sqrt{6}}{16} =\frac{16\sqrt{6}}{16} =\sqrt{6} $

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