(y-3)6y=4.5

Solution for (y-3)6y=4.5 equation:

(y-3)6y=4.5

We move all terms to the left:

(y-3)6y-(4.5)=0

We add all the numbers together, and all the variables

(y-3)6y-4.5=0

We multiply parentheses

6y^2-18y-4.5=0

a = 6; b = -18; c = -4.5;
Δ = b2-4ac
Δ = -182-4·6·(-4.5)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12\sqrt{3}}{2*6}=\frac{18-12\sqrt{3}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12\sqrt{3}}{2*6}=\frac{18+12\sqrt{3}}{12}
$