3y(5y+29)=18

Solution for 3y(5y+29)=18 equation:

3y(5y+29)=18

We move all terms to the left:

3y(5y+29)-(18)=0

We multiply parentheses

15y^2+87y-18=0

a = 15; b = 87; c = -18;
Δ = b2-4ac
Δ = 872-4·15·(-18)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-93}{2*15}=\frac{-180}{30}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+93}{2*15}=\frac{6}{30}
=1/5
$