1/(x+2)=2x-14

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Solution for 1/(x+2)=2x-14 equation:



1/(x+2)=2x-14
We move all terms to the left:
1/(x+2)-(2x-14)=0
Domain of the equation: (x+2)!=0
We move all terms containing x to the left, all other terms to the right
x!=-2
x∈R
We get rid of parentheses
1/(x+2)-2x+14=0
We multiply all the terms by the denominator
-2x*(x+2)+14*(x+2)+1=0
We multiply parentheses
-2x^2-4x+14x+28+1=0
We add all the numbers together, and all the variables
-2x^2+10x+29=0
a = -2; b = 10; c = +29;
Δ = b2-4ac
Δ = 102-4·(-2)·29
Δ = 332
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:
$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{83}}{2*-2}=\frac{-10-2\sqrt{83}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{83}}{2*-2}=\frac{-10+2\sqrt{83}}{-4} $

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