6/y-5=18)y+1

Solution for 6/y-5=18)y+1 equation:

6/y-5=18)y+1

We move all terms to the left:

6/y-5-(18)y+1)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-18y+6/y=0

We multiply all the terms by the denominator


-18y*y+6=0

Wy multiply elements

-18y^2+6=0

a = -18; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-18)·6
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-18}=\frac{0-12\sqrt{3}}{-36}
=-\frac{12\sqrt{3}}{-36}
=-\frac{\sqrt{3}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-18}=\frac{0+12\sqrt{3}}{-36}
=\frac{12\sqrt{3}}{-36}
=\frac{\sqrt{3}}{-3}
$