8/3-9/3x=11/2x-3

Solution for 8/3-9/3x=11/2x-3 equation:

8/3-9/3x=11/2x-3

We move all terms to the left:

8/3-9/3x-(11/2x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

-9/3x-11/2x+3+8/3=0

We calculate fractions


(-18x)/54x^2+(-297x)/54x^2+16x/54x^2+3=0

We multiply all the terms by the denominator


(-18x)+(-297x)+16x+3*54x^2=0

We add all the numbers together, and all the variables

16x+(-18x)+(-297x)+3*54x^2=0

Wy multiply elements

162x^2+16x+(-18x)+(-297x)=0

We get rid of parentheses

162x^2+16x-18x-297x=0

We add all the numbers together, and all the variables

162x^2-299x=0

a = 162; b = -299; c = 0;
Δ = b2-4ac
Δ = -2992-4·162·0
Δ = 89401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{89401}=299$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-299)-299}{2*162}=\frac{0}{324}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-299)+299}{2*162}=\frac{598}{324}
=1+137/162
$