5y(y-6)-4=0

Solution for 5y(y-6)-4=0 equation:

5y(y-6)-4=0

We multiply parentheses

5y^2-30y-4=0

a = 5; b = -30; c = -4;
Δ = b2-4ac
Δ = -302-4·5·(-4)
Δ = 980
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-14\sqrt{5}}{2*5}=\frac{30-14\sqrt{5}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+14\sqrt{5}}{2*5}=\frac{30+14\sqrt{5}}{10}
$