3y+5=3/2y

Solution for 3y+5=3/2y equation:

3y+5=3/2y

We move all terms to the left:

3y+5-(3/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3y-(+3/2y)+5=0

We get rid of parentheses

3y-3/2y+5=0

We multiply all the terms by the denominator


3y*2y+5*2y-3=0

Wy multiply elements

6y^2+10y-3=0

a = 6; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·6·(-3)
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*6}=\frac{-10-2\sqrt{43}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*6}=\frac{-10+2\sqrt{43}}{12}
$