2x+7/3x+8=14

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Solution for 2x+7/3x+8=14 equation:



2x+7/3x+8=14
We move all terms to the left:
2x+7/3x+8-(14)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
2x+7/3x-6=0
We multiply all the terms by the denominator
2x*3x-6*3x+7=0
Wy multiply elements
6x^2-18x+7=0
a = 6; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·6·7
Δ = 156
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:
$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{39}}{2*6}=\frac{18-2\sqrt{39}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{39}}{2*6}=\frac{18+2\sqrt{39}}{12} $

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