(3y-51)(3y-9)=180

Solution for (3y-51)(3y-9)=180 equation:

(3y-51)(3y-9)=180

We move all terms to the left:

(3y-51)(3y-9)-(180)=0

We multiply parentheses ..

(+9y^2-27y-153y+459)-180=0

We get rid of parentheses

9y^2-27y-153y+459-180=0

We add all the numbers together, and all the variables

9y^2-180y+279=0

a = 9; b = -180; c = +279;
Δ = b2-4ac
Δ = -1802-4·9·279
Δ = 22356
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:

$\sqrt{\Delta}=\sqrt{22356}=\sqrt{324*69}=\sqrt{324}*\sqrt{69}=18\sqrt{69}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-18\sqrt{69}}{2*9}=\frac{180-18\sqrt{69}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+18\sqrt{69}}{2*9}=\frac{180+18\sqrt{69}}{18}
$