5x=7x-14/x+2=0

Solution for 5x=7x-14/x+2=0 equation:

5x=7x-14/x+2=0

We move all terms to the left:

5x-(7x-14/x+2)=0


Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

5x-7x+14/x-2=0

We multiply all the terms by the denominator


5x*x-7x*x-2*x+14=0

We add all the numbers together, and all the variables

-2x+5x*x-7x*x+14=0

Wy multiply elements

5x^2-7x^2-2x+14=0

We add all the numbers together, and all the variables

-2x^2-2x+14=0

a = -2; b = -2; c = +14;
Δ = b2-4ac
Δ = -22-4·(-2)·14
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*-2}=\frac{2-2\sqrt{29}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*-2}=\frac{2+2\sqrt{29}}{-4}
$