(4y-4)3y=52

Solution for (4y-4)3y=52 equation:

(4y-4)3y=52

We move all terms to the left:

(4y-4)3y-(52)=0

We multiply parentheses

12y^2-12y-52=0

a = 12; b = -12; c = -52;
Δ = b2-4ac
Δ = -122-4·12·(-52)
Δ = 2640
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:

$\sqrt{\Delta}=\sqrt{2640}=\sqrt{16*165}=\sqrt{16}*\sqrt{165}=4\sqrt{165}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{165}}{2*12}=\frac{12-4\sqrt{165}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{165}}{2*12}=\frac{12+4\sqrt{165}}{24}
$