1/5y+1/2y=6/7

Solution for 1/5y+1/2y=6/7 equation:

1/5y+1/2y=6/7

We move all terms to the left:

1/5y+1/2y-(6/7)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

1/5y+1/2y-(+6/7)=0

We get rid of parentheses

1/5y+1/2y-6/7=0

We calculate fractions


(-120y^2)/490y^2+98y/490y^2+245y/490y^2=0

We multiply all the terms by the denominator


(-120y^2)+98y+245y=0

We add all the numbers together, and all the variables

(-120y^2)+343y=0

We get rid of parentheses

-120y^2+343y=0

a = -120; b = 343; c = 0;
Δ = b2-4ac
Δ = 3432-4·(-120)·0
Δ = 117649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{117649}=343$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(343)-343}{2*-120}=\frac{-686}{-240}
=2+103/120
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(343)+343}{2*-120}=\frac{0}{-240}
=0
$