10/9y=2+2y

Solution for 10/9y=2+2y equation:

10/9y=2+2y

We move all terms to the left:

10/9y-(2+2y)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We add all the numbers together, and all the variables

10/9y-(2y+2)=0

We get rid of parentheses

10/9y-2y-2=0

We multiply all the terms by the denominator


-2y*9y-2*9y+10=0

Wy multiply elements

-18y^2-18y+10=0

a = -18; b = -18; c = +10;
Δ = b2-4ac
Δ = -182-4·(-18)·10
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{29}}{2*-18}=\frac{18-6\sqrt{29}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{29}}{2*-18}=\frac{18+6\sqrt{29}}{-36}
$