3x-4/x+1=10

Solution for 3x-4/x+1=10 equation:

3x-4/x+1=10

We move all terms to the left:

3x-4/x+1-(10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-4/x-9=0

We multiply all the terms by the denominator


3x*x-9*x-4=0

We add all the numbers together, and all the variables

-9x+3x*x-4=0

Wy multiply elements

3x^2-9x-4=0

a = 3; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·3·(-4)
Δ = 129
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{-(-9)-\sqrt{129}}{2*3}=\frac{9-\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*3}=\frac{9+\sqrt{129}}{6}
$