2/3y+5=20-y

Solution for 2/3y+5=20-y equation:

2/3y+5=20-y

We move all terms to the left:

2/3y+5-(20-y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y-(-1y+20)+5=0

We get rid of parentheses

2/3y+1y-20+5=0

We multiply all the terms by the denominator


1y*3y-20*3y+5*3y+2=0

Wy multiply elements

3y^2-60y+15y+2=0

We add all the numbers together, and all the variables

3y^2-45y+2=0

a = 3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·3·2
Δ = 2001
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{-(-45)-\sqrt{2001}}{2*3}=\frac{45-\sqrt{2001}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2001}}{2*3}=\frac{45+\sqrt{2001}}{6}
$