2x(3-x/1x)=x+1

Solution for 2x(3-x/1x)=x+1 equation:

2x(3-x/1x)=x+1

We move all terms to the left:

2x(3-x/1x)-(x+1)=0


Domain of the equation: 1x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x(-x/1x+3)-(x+1)=0

We multiply parentheses

-2x^2+6x-(x+1)=0

We get rid of parentheses

-2x^2+6x-x-1=0

We add all the numbers together, and all the variables

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

a = -2; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-2)·(-1)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{17}}{2*-2}=\frac{-5-\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{17}}{2*-2}=\frac{-5+\sqrt{17}}{-4}
$