5/x+1=x-2

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

5/x+1=x-2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5/x-x+2+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x-x*x+5=0

Wy multiply elements

-1x^2+3x+5=0

a = -1; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-1)·5
Δ = 29
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{-(3)-\sqrt{29}}{2*-1}=\frac{-3-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*-1}=\frac{-3+\sqrt{29}}{-2}
$