8/3x+2=3/2x+11

Solution for 8/3x+2=3/2x+11 equation:

8/3x+2=3/2x+11

We move all terms to the left:

8/3x+2-(3/2x+11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+11)!=0

x∈R


We get rid of parentheses

8/3x-3/2x-11+2=0

We calculate fractions


16x/6x^2+(-9x)/6x^2-11+2=0

We add all the numbers together, and all the variables

16x/6x^2+(-9x)/6x^2-9=0

We multiply all the terms by the denominator


16x+(-9x)-9*6x^2=0

Wy multiply elements

-54x^2+16x+(-9x)=0

We get rid of parentheses

-54x^2+16x-9x=0

We add all the numbers together, and all the variables

-54x^2+7x=0

a = -54; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-54)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-54}=\frac{-14}{-108}
=7/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-54}=\frac{0}{-108}
=0
$