2/3y-y=5

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

2/3y-y=5

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -3; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·(-3)·2
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*-3}=\frac{15-\sqrt{249}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{249}}{2*-3}=\frac{15+\sqrt{249}}{-6}
$