1/3y-2=2y+2-9

Solution for 1/3y-2=2y+2-9 equation:

1/3y-2=2y+2-9

We move all terms to the left:

1/3y-2-(2y+2-9)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(2y-7)-2=0

We get rid of parentheses

1/3y-2y+7-2=0

We multiply all the terms by the denominator


-2y*3y+7*3y-2*3y+1=0

Wy multiply elements

-6y^2+21y-6y+1=0

We add all the numbers together, and all the variables

-6y^2+15y+1=0

a = -6; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-6)·1
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{249}}{2*-6}=\frac{-15-\sqrt{249}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*-6}=\frac{-15+\sqrt{249}}{-12}
$