3y+7=2/3(6y)

Solution for 3y+7=2/3(6y) equation:

3y+7=2/3(6y)

We move all terms to the left:

3y+7-(2/3(6y))=0


Domain of the equation: 36y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3y-(+2/36y)+7=0

We get rid of parentheses

3y-2/36y+7=0

We multiply all the terms by the denominator


3y*36y+7*36y-2=0

Wy multiply elements

108y^2+252y-2=0

a = 108; b = 252; c = -2;
Δ = b2-4ac
Δ = 2522-4·108·(-2)
Δ = 64368
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:

$\sqrt{\Delta}=\sqrt{64368}=\sqrt{144*447}=\sqrt{144}*\sqrt{447}=12\sqrt{447}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-12\sqrt{447}}{2*108}=\frac{-252-12\sqrt{447}}{216}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+12\sqrt{447}}{2*108}=\frac{-252+12\sqrt{447}}{216}
$