6(y-5)(6y-1)=0

Solution for 6(y-5)(6y-1)=0 equation:

6(y-5)(6y-1)=0

We multiply parentheses ..

6(+6y^2-1y-30y+5)=0

We multiply parentheses

36y^2-6y-180y+30=0

We add all the numbers together, and all the variables

36y^2-186y+30=0

a = 36; b = -186; c = +30;
Δ = b2-4ac
Δ = -1862-4·36·30
Δ = 30276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30276}=174$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-174}{2*36}=\frac{12}{72}
=1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+174}{2*36}=\frac{360}{72}
=5
$