y(6y-7)=0

Solution for y(6y-7)=0 equation:

y(6y-7)=0

We multiply parentheses

6y^2-7y=0

a = 6; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·6·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*6}=\frac{0}{12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*6}=\frac{14}{12}
=1+1/6
$