2y(5y+29)=12

Solution for 2y(5y+29)=12 equation:

2y(5y+29)=12

We move all terms to the left:

2y(5y+29)-(12)=0

We multiply parentheses

10y^2+58y-12=0

a = 10; b = 58; c = -12;
Δ = b2-4ac
Δ = 582-4·10·(-12)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-62}{2*10}=\frac{-120}{20}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+62}{2*10}=\frac{4}{20}
=1/5
$