1/3x+2+5=10-2x

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Solution for 1/3x+2+5=10-2x equation:



1/3x+2+5=10-2x
We move all terms to the left:
1/3x+2+5-(10-2x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
1/3x-(-2x+10)+2+5=0
We add all the numbers together, and all the variables
1/3x-(-2x+10)+7=0
We get rid of parentheses
1/3x+2x-10+7=0
We multiply all the terms by the denominator
2x*3x-10*3x+7*3x+1=0
Wy multiply elements
6x^2-30x+21x+1=0
We add all the numbers together, and all the variables
6x^2-9x+1=0
a = 6; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·6·1
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{57}}{2*6}=\frac{9-\sqrt{57}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*6}=\frac{9+\sqrt{57}}{12} $

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