2/3y+y=45

Solution for 2/3y+y=45 equation:

2/3y+y=45

We move all terms to the left:

2/3y+y-(45)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+2/3y-45=0

We multiply all the terms by the denominator


y*3y-45*3y+2=0

Wy multiply elements

3y^2-135y+2=0

a = 3; b = -135; c = +2;
Δ = b2-4ac
Δ = -1352-4·3·2
Δ = 18201
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{-(-135)-\sqrt{18201}}{2*3}=\frac{135-\sqrt{18201}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18201}}{2*3}=\frac{135+\sqrt{18201}}{6}
$