3y(y+9)=12y+13

Solution for 3y(y+9)=12y+13 equation:

3y(y+9)=12y+13

We move all terms to the left:

3y(y+9)-(12y+13)=0

We multiply parentheses

3y^2+27y-(12y+13)=0

We get rid of parentheses

3y^2+27y-12y-13=0

We add all the numbers together, and all the variables

3y^2+15y-13=0

a = 3; b = 15; c = -13;
Δ = b2-4ac
Δ = 152-4·3·(-13)
Δ = 381
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{381}}{2*3}=\frac{-15-\sqrt{381}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{381}}{2*3}=\frac{-15+\sqrt{381}}{6}
$