7y-9/y=18

Solution for 7y-9/y=18 equation:

7y-9/y=18

We move all terms to the left:

7y-9/y-(18)=0


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


7y*y-18*y-9=0

We add all the numbers together, and all the variables

-18y+7y*y-9=0

Wy multiply elements

7y^2-18y-9=0

a = 7; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·7·(-9)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-24}{2*7}=\frac{-6}{14}
=-3/7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+24}{2*7}=\frac{42}{14}
=3
$