5/3x+11=2x+9

Solution for 5/3x+11=2x+9 equation:

5/3x+11=2x+9

We move all terms to the left:

5/3x+11-(2x+9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-2x-9+11=0

We multiply all the terms by the denominator


-2x*3x-9*3x+11*3x+5=0

Wy multiply elements

-6x^2-27x+33x+5=0

We add all the numbers together, and all the variables

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

a = -6; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-6)·5
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*-6}=\frac{-6-2\sqrt{39}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*-6}=\frac{-6+2\sqrt{39}}{-12}
$