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 use the square of the difference formula

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

We get rid of parentheses

y^2-y+3-9-15=0

We add all the numbers together, and all the variables

y^2-1y-21=0

a = 1; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·1·(-21)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{85}}{2*1}=\frac{1-\sqrt{85}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*1}=\frac{1+\sqrt{85}}{2}
$