5y+5=12y^2-12y

Solution for 5y+5=12y^2-12y equation:

5y+5=12y^2-12y

We move all terms to the left:

5y+5-(12y^2-12y)=0

We get rid of parentheses

-12y^2+5y+12y+5=0

We add all the numbers together, and all the variables

-12y^2+17y+5=0

a = -12; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·(-12)·5
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*-12}=\frac{-40}{-24}
=1+2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*-12}=\frac{6}{-24}
=-1/4
$