4/(3y)+5/(2y)=1

Solution for 4/(3y)+5/(2y)=1 equation:

4/(3y)+5/(2y)=1

We move all terms to the left:

4/(3y)+5/(2y)-(1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We calculate fractions


8y/6y^2+15y/6y^2-1=0

We multiply all the terms by the denominator


8y+15y-1*6y^2=0

We add all the numbers together, and all the variables

23y-1*6y^2=0

Wy multiply elements

-6y^2+23y=0

a = -6; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-6)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-6}=\frac{-46}{-12}
=3+5/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-6}=\frac{0}{-12}
=0
$