6y2+22y+12=5y

Solution for 6y2+22y+12=5y equation:

6y^2+22y+12=5y

We move all terms to the left:

6y^2+22y+12-(5y)=0

We add all the numbers together, and all the variables

6y^2+17y+12=0

a = 6; b = 17; c = +12;
Δ = b2-4ac
Δ = 172-4·6·12
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-1}{2*6}=\frac{-18}{12}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+1}{2*6}=\frac{-16}{12}
=-1+1/3
$