15y+6y^2=27y

Solution for 15y+6y^2=27y equation:

15y+6y^2=27y

We move all terms to the left:

15y+6y^2-(27y)=0

We add all the numbers together, and all the variables

6y^2-12y=0

a = 6; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·6·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*6}=\frac{0}{12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*6}=\frac{24}{12}
=2
$