6/y=5/2y-7

Solution for 6/y=5/2y-7 equation:

6/y=5/2y-7

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y-7)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


12y/2y^2+(-5y)/2y^2+7=0

We multiply all the terms by the denominator


12y+(-5y)+7*2y^2=0

Wy multiply elements

14y^2+12y+(-5y)=0

We get rid of parentheses

14y^2+12y-5y=0

We add all the numbers together, and all the variables

14y^2+7y=0

a = 14; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·14·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*14}=\frac{-14}{28}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*14}=\frac{0}{28}
=0
$