1/y+1/4y-1/7=0

Solution for 1/y+1/4y-1/7=0 equation:

1/y+1/4y-1/7=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


(-16y^2)/196y^2+196y/196y^2+49y/196y^2=0

We multiply all the terms by the denominator


(-16y^2)+196y+49y=0

We add all the numbers together, and all the variables

(-16y^2)+245y=0

We get rid of parentheses

-16y^2+245y=0

a = -16; b = 245; c = 0;
Δ = b2-4ac
Δ = 2452-4·(-16)·0
Δ = 60025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{60025}=245$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(245)-245}{2*-16}=\frac{-490}{-32}
=15+5/16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(245)+245}{2*-16}=\frac{0}{-32}
=0
$