5/2y+7/3y=1

Solution for 5/2y+7/3y=1 equation:

5/2y+7/3y=1

We move all terms to the left:

5/2y+7/3y-(1)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We calculate fractions


15y/6y^2+14y/6y^2-1=0

We multiply all the terms by the denominator


15y+14y-1*6y^2=0

We add all the numbers together, and all the variables

29y-1*6y^2=0

Wy multiply elements

-6y^2+29y=0

a = -6; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-6)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-6}=\frac{-58}{-12}
=4+5/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-6}=\frac{0}{-12}
=0
$