6(y-3)(y-3)-(y-3)-15=0

Solution for 6(y-3)(y-3)-(y-3)-15=0 equation:

6(y-3)(y-3)-(y-3)-15=0

We get rid of parentheses

6(y-3)(y-3)-y+3-15=0

We multiply parentheses ..

6(+y^2-3y-3y+9)-y+3-15=0

We add all the numbers together, and all the variables

6(+y^2-3y-3y+9)-1y-12=0

We multiply parentheses

6y^2-18y-18y-1y+54-12=0

We add all the numbers together, and all the variables

6y^2-37y+42=0

a = 6; b = -37; c = +42;
Δ = b2-4ac
Δ = -372-4·6·42
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-19}{2*6}=\frac{18}{12}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+19}{2*6}=\frac{56}{12}
=4+2/3
$