11/2a+3=8/3a-4

Solution for 11/2a+3=8/3a-4 equation:

11/2a+3=8/3a-4

We move all terms to the left:

11/2a+3-(8/3a-4)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a-4)!=0

a∈R


We get rid of parentheses

11/2a-8/3a+4+3=0

We calculate fractions


33a/6a^2+(-16a)/6a^2+4+3=0

We add all the numbers together, and all the variables

33a/6a^2+(-16a)/6a^2+7=0

We multiply all the terms by the denominator


33a+(-16a)+7*6a^2=0

Wy multiply elements

42a^2+33a+(-16a)=0

We get rid of parentheses

42a^2+33a-16a=0

We add all the numbers together, and all the variables

42a^2+17a=0

a = 42; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·42·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*42}=\frac{-34}{84}
=-17/42
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*42}=\frac{0}{84}
=0
$