3(y+8)=2(10+3/2y)

Solution for 3(y+8)=2(10+3/2y) equation:

3(y+8)=2(10+3/2y)

We move all terms to the left:

3(y+8)-(2(10+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

3(y+8)-(2(3/2y+10))=0

We multiply parentheses

3y-(2(3/2y+10))+24=0

We multiply all the terms by the denominator


3y*2y+24*2y+10))-(2(3+10))=0

We add all the numbers together, and all the variables

3y*2y+24*2y+10))-(213)=0

We add all the numbers together, and all the variables

3y*2y+24*2y=0

Wy multiply elements

6y^2+48y=0

a = 6; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·6·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*6}=\frac{-96}{12}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*6}=\frac{0}{12}
=0
$