11=4x-1/3x

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

11=4x-1/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+33x+1=0

a = -12; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·(-12)·1
Δ = 1137
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{-(33)-\sqrt{1137}}{2*-12}=\frac{-33-\sqrt{1137}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1137}}{2*-12}=\frac{-33+\sqrt{1137}}{-24}
$