2/y=y/7y-24

Solution for 2/y=y/7y-24 equation:

2/y=y/7y-24

We move all terms to the left:

2/y-(y/7y-24)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 7y-24)!=0

y∈R


We get rid of parentheses

2/y-y/7y+24=0

We calculate fractions


(-1y^2)/7y^2+14y/7y^2+24=0

We multiply all the terms by the denominator


(-1y^2)+14y+24*7y^2=0

Wy multiply elements

(-1y^2)+168y^2+14y=0

We get rid of parentheses

-1y^2+168y^2+14y=0

We add all the numbers together, and all the variables

167y^2+14y=0

a = 167; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·167·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*167}=\frac{-28}{334}
=-14/167
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*167}=\frac{0}{334}
=0
$