2y(y-6)=5

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

2y(y-6)=5

We move all terms to the left:

2y(y-6)-(5)=0

We multiply parentheses

2y^2-12y-5=0

a = 2; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·2·(-5)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{46}}{2*2}=\frac{12-2\sqrt{46}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{46}}{2*2}=\frac{12+2\sqrt{46}}{4}
$