1/3x=4x+11

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

1/3x=4x+11

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-4x-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}
$