6+y=174/30y

Solution for 6+y=174/30y equation:

6+y=174/30y

We move all terms to the left:

6+y-(174/30y)=0


Domain of the equation: 30y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+174/30y)+6=0

We get rid of parentheses

y-174/30y+6=0

We multiply all the terms by the denominator


y*30y+6*30y-174=0

Wy multiply elements

30y^2+180y-174=0

a = 30; b = 180; c = -174;
Δ = b2-4ac
Δ = 1802-4·30·(-174)
Δ = 53280
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:

$\sqrt{\Delta}=\sqrt{53280}=\sqrt{144*370}=\sqrt{144}*\sqrt{370}=12\sqrt{370}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{370}}{2*30}=\frac{-180-12\sqrt{370}}{60}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{370}}{2*30}=\frac{-180+12\sqrt{370}}{60}
$