18y^2=1-3y

Solution for 18y^2=1-3y equation:

18y^2=1-3y

We move all terms to the left:

18y^2-(1-3y)=0

We add all the numbers together, and all the variables

18y^2-(-3y+1)=0

We get rid of parentheses

18y^2+3y-1=0

a = 18; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·18·(-1)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*18}=\frac{-12}{36}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*18}=\frac{6}{36}
=1/6
$