(2/3)(x+2)=20

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Solution for (2/3)(x+2)=20 equation:



(2/3)(x+2)=20
We move all terms to the left:
(2/3)(x+2)-(20)=0
Domain of the equation: 3)(x+2)!=0
x∈R
We add all the numbers together, and all the variables
(+2/3)(x+2)-20=0
We multiply parentheses ..
(+2x^2+2/3*2)-20=0
We multiply all the terms by the denominator
(+2x^2+2-20*3*2)=0
We get rid of parentheses
2x^2+2-20*3*2=0
We add all the numbers together, and all the variables
2x^2-118=0
a = 2; b = 0; c = -118;
Δ = b2-4ac
Δ = 02-4·2·(-118)
Δ = 944
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:
$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{59}}{2*2}=\frac{0-4\sqrt{59}}{4} =-\frac{4\sqrt{59}}{4} =-\sqrt{59} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{59}}{2*2}=\frac{0+4\sqrt{59}}{4} =\frac{4\sqrt{59}}{4} =\sqrt{59} $

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