(2/3)*x-4=20

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Solution for (2/3)*x-4=20 equation:



(2/3)*x-4=20
We move all terms to the left:
(2/3)*x-4-(20)=0
Domain of the equation: 3)*x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+2/3)*x-4-20=0
We add all the numbers together, and all the variables
(+2/3)*x-24=0
We multiply parentheses
2x^2-24=0
a = 2; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·2·(-24)
Δ = 192
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:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*2}=\frac{0-8\sqrt{3}}{4} =-\frac{8\sqrt{3}}{4} =-2\sqrt{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*2}=\frac{0+8\sqrt{3}}{4} =\frac{8\sqrt{3}}{4} =2\sqrt{3} $

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