2/3y+3/7y=5

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

2/3y+3/7y=5

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We calculate fractions


14y/21y^2+9y/21y^2-5=0

We multiply all the terms by the denominator


14y+9y-5*21y^2=0

We add all the numbers together, and all the variables

23y-5*21y^2=0

Wy multiply elements

-105y^2+23y=0

a = -105; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-105)·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*-105}=\frac{-46}{-210}
=23/105
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-105}=\frac{0}{-210}
=0
$