1-9x+4/x+1=0

Solution for 1-9x+4/x+1=0 equation:

1-9x+4/x+1=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-9x+4/x+2=0

We multiply all the terms by the denominator


-9x*x+2*x+4=0

We add all the numbers together, and all the variables

2x-9x*x+4=0

Wy multiply elements

-9x^2+2x+4=0

a = -9; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-9)·4
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*-9}=\frac{-2-2\sqrt{37}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*-9}=\frac{-2+2\sqrt{37}}{-18}
$