2/x+1=2x+5

Solution for 2/x+1=2x+5 equation:

2/x+1=2x+5

We move all terms to the left:

2/x+1-(2x+5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-2x-5+1=0

We multiply all the terms by the denominator


-2x*x-5*x+1*x+2=0

We add all the numbers together, and all the variables

-4x-2x*x+2=0

Wy multiply elements

-2x^2-4x+2=0

a = -2; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-2)·2
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*-2}=\frac{4-4\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*-2}=\frac{4+4\sqrt{2}}{-4}
$