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

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

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

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We multiply parentheses

y/3y+2y-14-6=0

We multiply all the terms by the denominator


y+2y*3y-14*3y-6*3y=0

Wy multiply elements

6y^2+y-42y-18y=0

We add all the numbers together, and all the variables

6y^2-59y=0

a = 6; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·6·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*6}=\frac{0}{12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*6}=\frac{118}{12}
=9+5/6
$