4x(2/3+Y)=16/3

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Solution for 4x(2/3+Y)=16/3 equation:



4x(2/3+)=16/3
We move all terms to the left:
4x(2/3+)-(16/3)=0
We add all the numbers together, and all the variables
4x(+2/3)-(+16/3)=0
We multiply parentheses
8x^2-(+16/3)=0
We get rid of parentheses
8x^2-16/3=0
We multiply all the terms by the denominator
8x^2*3-16=0
Wy multiply elements
24x^2-16=0
a = 24; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·24·(-16)
Δ = 1536
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:
$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*24}=\frac{0-16\sqrt{6}}{48} =-\frac{16\sqrt{6}}{48} =-\frac{\sqrt{6}}{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*24}=\frac{0+16\sqrt{6}}{48} =\frac{16\sqrt{6}}{48} =\frac{\sqrt{6}}{3} $

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