5x-2/x+1=0

Solution for 5x-2/x+1=0 equation:

5x-2/x+1=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+5x*x-2=0

Wy multiply elements

5x^2+x-2=0

a = 5; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·5·(-2)
Δ = 41
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{-(1)-\sqrt{41}}{2*5}=\frac{-1-\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*5}=\frac{-1+\sqrt{41}}{10}
$