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

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}
$