4/(x-1)+3x=11

Solution for 4/(x-1)+3x=11 equation:

4/(x-1)+3x=11

We move all terms to the left:

4/(x-1)+3x-(11)=0


Domain of the equation: (x-1)!=0

We move all terms containing x to the left, all other terms to the right

x!=1

x∈R


We add all the numbers together, and all the variables

3x+4/(x-1)-11=0

We multiply all the terms by the denominator


3x*(x-1)-11*(x-1)+4=0

We multiply parentheses

3x^2-3x-11x+11+4=0

We add all the numbers together, and all the variables

3x^2-14x+15=0

a = 3; b = -14; c = +15;
Δ = b2-4ac
Δ = -142-4·3·15
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4}{2*3}=\frac{10}{6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4}{2*3}=\frac{18}{6}
=3
$