30/y-18/2y=7

Solution for 30/y-18/2y=7 equation:

30/y-18/2y=7

We move all terms to the left:

30/y-18/2y-(7)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We calculate fractions


60y/2y^2+(-18y)/2y^2-7=0

We multiply all the terms by the denominator


60y+(-18y)-7*2y^2=0

Wy multiply elements

-14y^2+60y+(-18y)=0

We get rid of parentheses

-14y^2+60y-18y=0

We add all the numbers together, and all the variables

-14y^2+42y=0

a = -14; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-14)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-14}=\frac{-84}{-28}
=+3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-14}=\frac{0}{-28}
=0
$