5/3x+11=x+2

Solution for 5/3x+11=x+2 equation:

5/3x+11=x+2

We move all terms to the left:

5/3x+11-(x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-x-2+11=0

We multiply all the terms by the denominator


-x*3x-2*3x+11*3x+5=0

Wy multiply elements

-3x^2-6x+33x+5=0

We add all the numbers together, and all the variables

-3x^2+27x+5=0

a = -3; b = 27; c = +5;
Δ = b2-4ac
Δ = 272-4·(-3)·5
Δ = 789
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{-(27)-\sqrt{789}}{2*-3}=\frac{-27-\sqrt{789}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{789}}{2*-3}=\frac{-27+\sqrt{789}}{-6}
$