3/2y+1=4/3y+16

Solution for 3/2y+1=4/3y+16 equation:

3/2y+1=4/3y+16

We move all terms to the left:

3/2y+1-(4/3y+16)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y+16)!=0

y∈R


We get rid of parentheses

3/2y-4/3y-16+1=0

We calculate fractions


9y/6y^2+(-8y)/6y^2-16+1=0

We add all the numbers together, and all the variables

9y/6y^2+(-8y)/6y^2-15=0

We multiply all the terms by the denominator


9y+(-8y)-15*6y^2=0

Wy multiply elements

-90y^2+9y+(-8y)=0

We get rid of parentheses

-90y^2+9y-8y=0

We add all the numbers together, and all the variables

-90y^2+y=0

a = -90; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-90)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-90}=\frac{-2}{-180}
=1/90
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-90}=\frac{0}{-180}
=0
$