4/2y-1=7-3/y

Solution for 4/2y-1=7-3/y equation:

4/2y-1=7-3/y

We move all terms to the left:

4/2y-1-(7-3/y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

4/2y-(-3/y+7)-1=0

We get rid of parentheses

4/2y+3/y-7-1=0

We calculate fractions


4y/2y^2+6y/2y^2-7-1=0

We add all the numbers together, and all the variables

4y/2y^2+6y/2y^2-8=0

We multiply all the terms by the denominator


4y+6y-8*2y^2=0

We add all the numbers together, and all the variables

10y-8*2y^2=0

Wy multiply elements

-16y^2+10y=0

a = -16; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-16)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-16}=\frac{-20}{-32}
=5/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-16}=\frac{0}{-32}
=0
$