6y=174/30y

Solution for 6y=174/30y equation:

6y=174/30y

We move all terms to the left:

6y-(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

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

We get rid of parentheses

6y-174/30y=0

We multiply all the terms by the denominator


6y*30y-174=0

Wy multiply elements

180y^2-174=0

a = 180; b = 0; c = -174;
Δ = b2-4ac
Δ = 02-4·180·(-174)
Δ = 125280
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:

$\sqrt{\Delta}=\sqrt{125280}=\sqrt{144*870}=\sqrt{144}*\sqrt{870}=12\sqrt{870}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{870}}{2*180}=\frac{0-12\sqrt{870}}{360}
=-\frac{12\sqrt{870}}{360}
=-\frac{\sqrt{870}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{870}}{2*180}=\frac{0+12\sqrt{870}}{360}
=\frac{12\sqrt{870}}{360}
=\frac{\sqrt{870}}{30}
$