2/3y+3/8y=5

Solution for 2/3y+3/8y=5 equation:

2/3y+3/8y=5

We move all terms to the left:

2/3y+3/8y-(5)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We calculate fractions


16y/24y^2+9y/24y^2-5=0

We multiply all the terms by the denominator


16y+9y-5*24y^2=0

We add all the numbers together, and all the variables

25y-5*24y^2=0

Wy multiply elements

-120y^2+25y=0

a = -120; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-120)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-120}=\frac{-50}{-240}
=5/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-120}=\frac{0}{-240}
=0
$