3x-11/x+1=2x-24

Solution for 3x-11/x+1=2x-24 equation:

3x-11/x+1=2x-24

We move all terms to the left:

3x-11/x+1-(2x-24)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3x-11/x-2x+24+1=0

We multiply all the terms by the denominator


3x*x-2x*x+24*x+1*x-11=0

We add all the numbers together, and all the variables

25x+3x*x-2x*x-11=0

Wy multiply elements

3x^2-2x^2+25x-11=0

We add all the numbers together, and all the variables

x^2+25x-11=0

a = 1; b = 25; c = -11;
Δ = b2-4ac
Δ = 252-4·1·(-11)
Δ = 669
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{-(25)-\sqrt{669}}{2*1}=\frac{-25-\sqrt{669}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{669}}{2*1}=\frac{-25+\sqrt{669}}{2}
$