(1/3)x+(5/8)x=46

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Solution for (1/3)x+(5/8)x=46 equation:



(1/3)x+(5/8)x=46
We move all terms to the left:
(1/3)x+(5/8)x-(46)=0
Domain of the equation: 3)x!=0
x!=0/1
x!=0
x∈R
Domain of the equation: 8)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+1/3)x+(+5/8)x-46=0
We multiply parentheses
x^2+5x^2-46=0
We add all the numbers together, and all the variables
6x^2-46=0
a = 6; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·6·(-46)
Δ = 1104
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:
$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{69}}{2*6}=\frac{0-4\sqrt{69}}{12} =-\frac{4\sqrt{69}}{12} =-\frac{\sqrt{69}}{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{69}}{2*6}=\frac{0+4\sqrt{69}}{12} =\frac{4\sqrt{69}}{12} =\frac{\sqrt{69}}{3} $

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