6y(2y-5)=0

Solution for 6y(2y-5)=0 equation:

6y(2y-5)=0

We multiply parentheses

12y^2-30y=0

a = 12; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·12·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*12}=\frac{0}{24}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*12}=\frac{60}{24}
=2+1/2
$