4+1/3x=2x-11

Solution for 4+1/3x=2x-11 equation:

4+1/3x=2x-11

We move all terms to the left:

4+1/3x-(2x-11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x+11+4=0

We multiply all the terms by the denominator


-2x*3x+11*3x+4*3x+1=0

Wy multiply elements

-6x^2+33x+12x+1=0

We add all the numbers together, and all the variables

-6x^2+45x+1=0

a = -6; b = 45; c = +1;
Δ = b2-4ac
Δ = 452-4·(-6)·1
Δ = 2049
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{-(45)-\sqrt{2049}}{2*-6}=\frac{-45-\sqrt{2049}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2049}}{2*-6}=\frac{-45+\sqrt{2049}}{-12}
$