2y(3y+2)=46

Solution for 2y(3y+2)=46 equation:

2y(3y+2)=46

We move all terms to the left:

2y(3y+2)-(46)=0

We multiply parentheses

6y^2+4y-46=0

a = 6; b = 4; c = -46;
Δ = b2-4ac
Δ = 42-4·6·(-46)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{70}}{2*6}=\frac{-4-4\sqrt{70}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{70}}{2*6}=\frac{-4+4\sqrt{70}}{12}
$