4y(5y+3)=186

Solution for 4y(5y+3)=186 equation:

4y(5y+3)=186

We move all terms to the left:

4y(5y+3)-(186)=0

We multiply parentheses

20y^2+12y-186=0

a = 20; b = 12; c = -186;
Δ = b2-4ac
Δ = 122-4·20·(-186)
Δ = 15024
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:

$\sqrt{\Delta}=\sqrt{15024}=\sqrt{16*939}=\sqrt{16}*\sqrt{939}=4\sqrt{939}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{939}}{2*20}=\frac{-12-4\sqrt{939}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{939}}{2*20}=\frac{-12+4\sqrt{939}}{40}
$