27/18y=10y

Solution for 27/18y=10y equation:

27/18y=10y

We move all terms to the left:

27/18y-(10y)=0


Domain of the equation: 18y!=0

y!=0/18

y!=0

y∈R


We add all the numbers together, and all the variables

-10y+27/18y=0

We multiply all the terms by the denominator


-10y*18y+27=0

Wy multiply elements

-180y^2+27=0

a = -180; b = 0; c = +27;
Δ = b2-4ac
Δ = 02-4·(-180)·27
Δ = 19440
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:

$\sqrt{\Delta}=\sqrt{19440}=\sqrt{1296*15}=\sqrt{1296}*\sqrt{15}=36\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{15}}{2*-180}=\frac{0-36\sqrt{15}}{-360}
=-\frac{36\sqrt{15}}{-360}
=-\frac{\sqrt{15}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{15}}{2*-180}=\frac{0+36\sqrt{15}}{-360}
=\frac{36\sqrt{15}}{-360}
=\frac{\sqrt{15}}{-10}
$