(1/3)(x+7)=5

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Solution for (1/3)(x+7)=5 equation:



(1/3)(x+7)=5
We move all terms to the left:
(1/3)(x+7)-(5)=0
Domain of the equation: 3)(x+7)!=0
x∈R
We add all the numbers together, and all the variables
(+1/3)(x+7)-5=0
We multiply parentheses ..
(+x^2+1/3*7)-5=0
We multiply all the terms by the denominator
(+x^2+1-5*3*7)=0
We get rid of parentheses
x^2+1-5*3*7=0
We add all the numbers together, and all the variables
x^2-104=0
a = 1; b = 0; c = -104;
Δ = b2-4ac
Δ = 02-4·1·(-104)
Δ = 416
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:
$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*1}=\frac{0-4\sqrt{26}}{2} =-\frac{4\sqrt{26}}{2} =-2\sqrt{26} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*1}=\frac{0+4\sqrt{26}}{2} =\frac{4\sqrt{26}}{2} =2\sqrt{26} $

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