2/3y+3y-1=219

Solution for 2/3y+3y-1=219 equation:

2/3y+3y-1=219

We move all terms to the left:

2/3y+3y-1-(219)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

3y+2/3y-220=0

We multiply all the terms by the denominator


3y*3y-220*3y+2=0

Wy multiply elements

9y^2-660y+2=0

a = 9; b = -660; c = +2;
Δ = b2-4ac
Δ = -6602-4·9·2
Δ = 435528
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:

$\sqrt{\Delta}=\sqrt{435528}=\sqrt{36*12098}=\sqrt{36}*\sqrt{12098}=6\sqrt{12098}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-660)-6\sqrt{12098}}{2*9}=\frac{660-6\sqrt{12098}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-660)+6\sqrt{12098}}{2*9}=\frac{660+6\sqrt{12098}}{18}
$